Run Visio. To create a new drawing you can choose from a list of templates. These provide built-in drawing objects to make the creating of diagrams easier and faster. To start select the ‘Basic Diagram (Metric)’. This will open a blank page. On the left-hand side of the screen are three lists of shapes (‘stencils’).
Whichever template you choose when you open a new file, you can always open more stencils at a later stage. Use FILE|SHAPES to do this.
One way you can draw in Visio is to use these predefined shapes. You will use Visio Help to find out more information on drawing with these. Move the cursor over a shape in a stencil. A bubble will appear as shown below. Select More… and read through all the information given in the Shape Basics help page. Practice briefly as you go along - there are questions below.
Copy some shapes onto a page. Check that you know the answers to the following questions.
Pressing the Ctrl and Shift keys together changes the cursor to Zoom In/Out mode. Pressing the left mouse button zooms in – centring on the point where you have clicked. Similarly, pressing the right mouse button zooms out. To zoom in on a particular area of a drawing, move the cursor to one corner, press Ctrl and Shift, press the left mouse key and drag a box around the area in question, and Visio will zoom in on that section.
Press Ctrl and Shift, press the right mouse key, and drag the mouse to “pan” around – i.e. to change what section of the page is shown on screen.
Place some shapes on your current page. Choose VIEW|PAN AND ZOM WINDOW. A window will open which allows you to quickly change what is being shown. Drag the mouse to select what area of the drawing page is shown. A red rectangle will appear. Simply drag the red rectangle around or change its size (by dragging a corner or side) to change what is shown on screen.
Shapes can be grouped together. This makes it easier to resize and rotate drawing shapes that go together. Select the shapes you want to group and choose SHAPE|GROUPING|GROUP or press . Select a group and choose SHAPE|GROUPING|UNGROUP to separate the shapes in a group.
In many cases you may wish to move a shape just horizontally or vertically. You can do this by selecting the shape and using the arrow keys to move it. Keeping the Shift key pressed allows finer positioning. If you use the mouse then it may be harder to control (e.g. you might move it a little upwards accidentally when you only wanted to move it horizontally). If you keep a Shift key pressed when you move a shape with the mouse it will only move horizontally, vertically or at 45°. This can be a very useful feature. Try it out.
The two drawings below are made from the same shapes (a square and a circle). The difference is due to the order in which the shapes were added – the later shapes are always on top. You can adjust the order by selecting a shape and using the options on the SHAPE|ORDER menu or .
A shape or group of shapes (either shapes grouped using or simply a number of shapes selected together) can be rotated through 90° or flipped horizontally or vertically using the SHAPE|ROTATE OR FLIP menu options or .
As well as using snap and glue options (see below) you can align a number of objects using the SHAPE|ALIGN SHAPES dialog box. Select the shapes, choose the menu option, and then select the way you want the shapes to be aligned.
You will see below how to draw shapes not
given in any stencil using lines etc. An alternative is to combine existing
shapes to get the shape you want. As an example, everything below was produced
using squares and circles. These and other shapes can be created easily using
Sometimes it is necessary to create an array of shapes (see below). One way to do this is as follows:
Copy one shape onto your page. Press Ctrl and drag it sideways to create a second copy. If you press Shift, then Ctrl, and then drag, the copy will only move horizontally or vertically. If not already selected then select the second copy. Press F4 – this will repeat the action to create a third copy. Keep pressing F4 until a row is complete. Now select the whole first row and copy to create a second row. Press F4 to create a third row and so on.
Alternatively select the shape to be copied. Choose TOOLS|ADD-ONS|VISIO EXTRAS|ARRAY SHAPES. Enter the number of rows and columns and the spacing required. Then press OK.
As seen above text can be added to any shape by selecting it and typing. You can also add text anywhere on a page by using the Text Tool . Select this tool and click wherever you want the text to be positioned. Then type. To edit a piece of text, if you have already selected the Text Tool, just click on it. If you have the Pointer Tool currently selected then double-click on the text. Text can be formatted using all the standard options from the toolbar, using FORMAT|TEXT, or from the right-click menu.
The size of text can be easily changed using the Increase Font Size and Decrease Font Size buttons .
If you select a shape and do any of these formatting actions then all the text associated with the shape will be reformatted.
The Snap and Glue facilities make can make accurate drawing easy and fast but they do take a little bit of getting used to. First select VIEW|TOOLBARS|SNAP AND GLUE. The Snap and Glue toolbar will appear . You must understand the following definitions first.
The Rulers are shown above and to the side of the page. The Grid is shown on the page but is not part of the drawing. The fineness/coarseness of the rulers and grid can be adjusted by choosing TOOLS|RULER & GRID.
Guides are vertical or horizontal lines that can be placed on a drawing but are not part of the drawing. To place a Guide, click on the horizontal or vertical ruler and drag a Guide onto the page. A Guide line will appear along with a Guide Point. The guide point can be moved if necessary by dragging it along the line. Shapes can be aligned using Guides as will be seen below.
Guides do not have to be horizontal or vertical. When you rotate a Guide the Guide Point acts as the centre of rotation. You may wish to move it before rotating. Then choose VIEW|SIZE & POSITION WINDOW and enter the desired angle.
Snap behaviour in Visio positions and aligns shapes exactly. Snapping pulls shapes to one another or to ruler subdivisions, grid lines, or guides so you can control placement and alignment. You can control what types of objects shapes snap to and the snap strength, which is the amount of pull that an object exerts. By default, shapes snap to both ruler subdivisions and grid lines. To snap shapes more easily to ruler subdivisions, turn off snapping to grid lines .
Note that you may not always want snapping. For example, by turning off snapping, you may find it easier to draw smooth freeform curves (see below).
To understand what is meant by snapping the best thing to do is to turn off snapping by pressing the Toggle Snap button . Now add a shape and resize it. Also draw a line. Now press the button again to switch snapping back on and do the same things.
Note that if snapping is off then the level of control over position depends on the level of zoom selected. At one level of zoom you may be able to position to within half a millimetre (see the position on the status bar). By zooming in closer you will be able to position to within a tenth of a millimetre and finer. You can also position to whatever level of accuracy you want at any time using VIEW|SIZE & POSITION WINDOW.
As an example, suppose you wish to draw a number of items all 16.3 mm wide. Position a vertical Guide line on the screen. Note its position (from the status bar). Then switch off snapping and position another Guide 16.3 mm away from the first. Now drag the shapes onto the page. Switch snapping back on. Line their edges up one-by-one with one Guide (they should snap to it) and then resize them until the opposite sides of the shapes snap to the other Guide. This is a quick and accurate way of drawing shapes which have dimensions that are not round numbers.
Make sure that Glue to Connection Points is selected (it’s a default selection). Then add two Rectangle shapes as shown below left. Use the Connector Tool to join a connection point on one to a connection point on the other as shown below centre. To do this, click on one connection point (it should turn red to indicate gluing) and drag to the other. The Connector is now ‘glued’ to the connection points on the shapes. Move a shape and the connector will move automatically (see below right).
You can glue shapes to Guides so that they will all move if the Guide is moved.
The Glue to Shape Geometry option allows you to glue a Connector (or any line) to any point on a shape. When the shape is moved the line will stay connected to that point.
Flowcharts are used to represent clearly the steps in a process. They are used for designing software, manufacturing processes, and in other areas where it is useful to break complex processes into simpler steps. They are helpful when explaining processes to others and also for identifying potential problems with processes. Visio is designed to make the drawing of flowcharts easy.
Flowcharts are drawn in a standard way using standard symbols and you should stick to these. An example is shown below.
This example has three standard flowchart shapes. Terminators are used to start/end the process. These are sometimes labelled simply START and END. An Action or Process box represents a single step. A Decision diamond represents where a decision is made. Different decision outcomes emerge from different points on the diamond. These are the most commonly used shapes but a full range is available from a Visio stencil.
Open the FILE|SHAPES|FLOWCHARTS|BASIC FLOWCHART SHAPES (METRIC) stencil. Drag the various shapes onto the page for the flowchart above. Locate them roughly as shown. Use snapping to keep them in a line. Type the text and alter the font size if necessary. Alter the shape sizes if they are too small for the font. Use the connector tool to connect the shapes. Start with one connector. Change the line width if you wish and add an arrow to the end. Change the arrow size if necessary. Don’t repeat this process for each arrow – simply copy the one you have formatted and use it to make the other connections. Note that if you select a connector, points on it are highlighted. You can drag these to adjust the route it takes if necessary. Now add the ‘Yes’ and ‘No’ to the connectors (or ‘Flow Lines’) coming from the two Decision shapes. Change the fill property of the shapes and add a title.
This should not take you long if you go about it sensibly. If it is taking you a long time then perhaps there is a faster way of doing it. Ask for help if necessary.
This section looks at producing shapes not included in any stencil. It first looks, however, at how to alter shapes added to a drawing.
Select a shape (like the square below) and select the Line Tool . The vertices are highlighted as shown below.
Moving the mouse pointer over any vertex changes it to a four-sided arrow indicating that that vertex can be dragged to a new position. Note that the currently selected vertex is highlighted. Pressing Delete when a vertex is highlighted will remove it from a shape. Note that a connection point does not move when an associated vertex is moved. Once the Line Tool is selected Visio stays in that mode until another tool is selected. Select the Pointer Tool to get back to normal operation.
The Line Tool can also be used to add a vertex to a shape. Select a shape. Choose the Line Tool. Press Ctrl and click on a line in the shape. An extra vertex will be added at that point. The vertex can then be moved to change the shape. For example, a square can be changed to that shown below by adding a vertex.
Note that more than one vertex can be moved at a time. Use Shift and click to select more than one. Moving one will then move all the selected vertices.
Selecting a shape using the Pencil Tool highlights the vertices but also the ‘Control points’.
Moving a control point causes the associated line to form an arc as shown below. If a line is curved then the control point is larger than it is for a line that is straight (see below). Note that vertices can be added, deleted, and moved with the Pencil Tool in the same way as with the Line Tool.
The Line Tool and Pencil Tool can both be used to draw ‘polylines’ or shapes from scratch. A ‘shape’ is defined here as a closed series of straight lines and/or curves. A ‘polyline’ may be composed of many line and/or curve segments but is not closed. The picture below shows a shape and a polyline. A polyline does not have a fill colour whereas a shape can be filled with whatever colour you want.
To draw a polyline select either the Line or Pencil tool. Click on the first point and then drag to the next. Release the mouse button. Click again and drag again to get a second line segment. Repeat until the polyline is finished. If the last line segment ends at the start of the first line segment (i.e. if you connect the two ends of the polyline together) then it becomes a shape automatically with the current fill colour . When a polyline or shape is complete you can add/remove points and move points as shown above.
The Rectangle and Ellipse Tools can be used to draw rectangles and ellipses. Select the tool you want, click where you want one corner and drag to produce the shape. The dimensions are given on the status bar as you draw. The shapes can be altered as before. The shape below was produced by first using the Ellipse Tool to draw a circle. The Pencil Tool was then used to add three points to the circumference and then the middle point was moved
The Arc Tool can be used in the same way as the Line and Pencil tools to draw polylines and shapes. It was seen above that by moving the control point of a line it could be turned into an arc. Those arcs were always parts of circles however (see below left). The arcs drawn with the arc tool are parts of ellipses (see below right). That means that they can be ‘eccentric’.
As mentioned above the Arc Tool can be used to create a polyline of arcs (see below left). Switching to the Pencil Tool shows the control points as before (see below right).
The only difference is that each arc segment has extra ‘eccentricity handles’. These are two extra points on either side of the control point and joined to it by a straight line. They become visible when you select a control point (see below left). The closer the handles are to the control point, the less eccentric the curve is (i.e. the closer it is to being circular) - see below centre. The handles can be dragged in the same way as a vertex or control point. The ‘angle of eccentricity’ can be changed by dragging an eccentricity handle around the control point (see below right). These give you a great deal of control over the shapes you draw but they do take a little bit of getting used to.
The Freeform Tool can be used to draw curves of any shape using the mouse. Click and drag the mouse in the way you want the curve to appear. Note that this can be difficult to do – there is an alternative shown below. It may be helpful to switch of Snapping before using the Freeform Tool.
Note that freeform curves cannot form a closed shape - the two ends must be in different locations. A freeform curve can be part of a closed shape, however. The upper line of the shape below was drawn using the Freeform Tool. Then the Pencil Tool was selected. Clicking on the end of the freeform curve and dragging adds a line to it. Three lines were added to create the shape shown.
A freeform curve has two vertices as well as control points along its length, all of which can be moved. They also have two handles, one connected to each end point, which can be moved to set the angles at the ends of the line. Moving the handle away from the vertex changes the eccentricity of the curve.
Note that a polyline can be drawn using freeform curves. The polyline below left is made of two freeform curves. Note the discontinuity (jump in slope) where the two curves meet. This can be removed by making sure the slope of each line is the same at the point of connection (see below right).
NOTE: The Freeform Tool can be difficult to use but is often the most suitable way of drawing a complex shape. NEVER try and get it right first time - it’s too difficult to do. Instead, draw what you want roughly using the mouse and then move the points around as necessary.
NOTE: When you draw a shape roughly, make sure it is as complex as the shape you want (i.e. that it has at least as many twists and turns). Why is this? Because you cannot add control points to a freeform curve once it’s drawn. If you press Ctrl and click on the curve, a new vertex will be added – not a new control point - this means that the curve is split in two (i.e. it’s no longer continuous). Try this out.
If your rough freeform curve has too many control points then it can take a long time to move them to where you want them. You can delete any one by selecting it and pressing Delete. The fewer points there are, the easier it will be to adjust the shape – but if you delete too many then you won’t be able to get the shape you want - and you can’t add new ones - so BE CAREFUL.
This will all make more sense with an example. Try drawing the front of an aircraft as shown below. Start with something very rough. In this case you want the line to be horizontal at the two end-points so adjust the slopes at those points first. Then move (and delete) points as required to get the shape you want.
If you select one or more overlapping lines/arcs/curves/polylines as below left and select SHAPE|OPERATIONS|TRIM, the lines will be trimmed where they meet. In the picture below centre the trimmed segments have been moved to make things clear. The two remaining lines can be made into a closed shape by selecting them and choosing SHAPE|OPERATIONS|JOIN.
Select a shape/curve/polyline (see below left) and choose SHAPE|OPERATIONS|OFFSET. Enter a distance in the dialog box (5 mm for example below). Two new shapes/curves/polylines will be produced which are that distance from the original curve on either side of it.
It can be difficult to use the mouse to draw a freeform curve accurately. If there are a number of points on the screen that the curve must pass through then here is an alternative. Draw a polyline with its vertices at those points. Select the line and choose SHAPE|OPERATIONS|FIT CURVE. Select the default settings. An example is given below – the original line is on the left and the freeform curve is on the right (with the original line shown in gray).
This can also be done with closed polylines and is a quick way to produce some complex shapes (see below).
Now is the time to revise what the following toolbar buttons do. Select lines and shapes and play around with them. The same formatting can be done using the FORMAT menu or by right-clicking on an object.
FORMAT|LINE also allows you to alter the size of arrows and whether lines are rounded at the end:
IMPORTANT: The current default format settings are indicated on the toolbar – e.g. what the font size is, what the line colour is, etc. When you, for example, draw a line, it’s properties are the same as the current settings. There are two ways of changing the properties of a line (or text, etc.):
1: You can draw the line, then select it and change the properties, or;
2: You can change the current properties to the settings desired and then draw the line.
To understand the second option, follow this example: You will draw a number of red arrows. You could draw lines and then change their properties but in this case you will set the properties first. Make sure nothing is selected (if something is selected then click somewhere else on the page first). Now use the Line Color and Arrow buttons to select red lines with an arrow on the end. You have changed the current settings so when you draw lines using the Line Tool they will have those properties.
Note that changing the properties of an object (by selecting it and then changing them) does not affect the current properties.
Note also that the current properties do not affect shapes dragged onto the drawing page. If you want a red square then drag a square shape onto the page (the square will be black no matter what the current settings are) and then change it to red.
Visio allows you to calculate the area and circumference of any selected shape. Select the shape and choose TOOLS|ADD-ONS|VISIO EXTRAS||SHAPE AREA AND PERIMETER…
One or more connection points can be added to any shape. Select the shape. Choose the Connection Point Tool (see below). Press Ctrl and click on the shape where you want the connection points to be. You can now glue lines or Connectors to these connection points (see above).
How would you draw the shape on the right below?
Firstly it is symmetric so it is much quicker to draw one half and copy it. Draw a freehand curve as shown (see above). Adjust it if necessary (see above). Add a straight line for the top (see above). Make a copy and flip it to form the outline (see above). Join the polylines using SHAPE|OPERATIONS|JOIN. Then change the fill colour and set the Line Colour to No Line.
How would you draw the shape on the right below quickly (and accurately if you know the required dimensions)?
Here is one suggestion. Use two rectangles of the desired dimensions as shown below. Move one over the other. Then round the corners of one - this tool gives you the option of specifying the radius of the corners in millimetres. Now use SHAPE|OPERATIONS|UNION to merge the shapes into one.
Is this quicker than using the Pencil Tool?
How would you make the following shape quickly and accurately (assuming you know the desired dimensions)?
How would you make the shape below right (step 4)? One way is illustrated here. Draw a circle and a rectangle (step 1). The rectangle has no line, is filled with black, and has its Transparency set to 50% (FORMAT|FILL). Make a copy of the circle and position one circle and the rectangle as shown (step 2). Use SHAPE|OPERATIONS|INTERSECT to create the half circle shown – the rectangle and one circle will be lost. Then move the half circle over the remaining circle (step 4). It is black but transparent so it simply darkens what is behind it.
Can you think of a quicker way of doing this?
The drawing on the right was created by first drawing an ellipse and formatting it as shown below left. Then two shapes were drawn over it using the Arc Tool (see below centre). All three shapes were selected and SHAPE|OPERATIONS|FRAGMENT chosen. The unwanted shapes created were deleted and the two shapes had their fill colours changed.
A wide range of Fill colours are available. It is easiest to use FORMAT|FILL because this gives a list of all colours previously used in a drawing (see below left). At the end of the list is the More Colors… option which opens up another dialog box (below right) where you can choose from over a million different shades. Drag to select a basic colour and then use the triangle to select the brightness.
Different fill patterns can be used to create shading (see below left). Select the Pattern and the Pattern Color in the Fill dialog box in order to create the desired effect (see below centre). The glasses (below right) are filled but are partially transparent.
A diagram is used to illustrate/explain something. Unlike a technical drawing, a diagram does not need accurate dimensions – indeed it may be necessary to exaggerate certain dimensions in order to illustrate something clearly. The following diagram shows a ball rolling off a desk. The trajectory is shown and the numbers make the sequence through time clear. The lighting effect on the ball was done using the Fill Pattern menu . Try reproducing this diagram. Think first how you will do each part as quickly as possible. Good planning can save a lot of time.
You can use layers to organize related shapes on a drawing page. A layer is a named category of shapes. By assigning shapes to different layers, you can selectively view, print, colour, and lock different categories of shapes, as well as control whether you can snap to or glue to shapes on a layer.
For example, when you're doing an technical drawing, the title block might be assigned to one layer, the main drawing to another, and the dimensions to a third layer. That way, when you work with the dimensions you can lock the other layers so that you don't have to worry about accidentally rearranging the main drawing.
To learn more try this example. Draw a large rectangle on the screen. Set it so that it has no Fill. This will form a border for your drawing. This will be on a layer of its own. To create a new layer called ‘Background’ and to assign the rectangle to it, select the rectangle and choose FORMAT|LAYER. A dialog box will appear with a list of existing layers. This indicates which layer the selected object is on (none currently). Press New and type ‘Background’ as the name of a new layer. Press OK. A Background layer has now been created and the rectangle is assigned to it.
You will now do a drawing on a new ‘Main’ layer. You will add a number of shapes. You don’t want to have to assign each shape to this new layer one-by-one so make it an Active Layer. There should currently be no Active Layer. When you add a shape it is automatically assigned to whatever layers are Active.
Choose VIEW|LAYER PROPERITES. A dialog box
will appear. Press New and type ‘
Add a number of shapes to the page (see below). You will notice that when any shape is selected the layer it is assigned to is indicated on the toolbar . You can use this indicator to quickly change which layer the selected shape is assigned to. Note that ‘Background’ will not appear on the list because you have Locked it.
Now add labels for each item on the drawing and put these labels on a separate layer. Once this is done you can use VIEW|PROPERTIES to switch on/off whether each layer is visible or not.
Where else might you use Layers?
You could add notes to a drawing which will be visible to anyone who opens a drawing but which will not print.
If you are drawing a factory layout you may have a very large amount of information – walls, doors, windows on one layer, machinery on another, electrical systems on another, pneumatic systems on another. When all the information is on the drawing it may be cluttered but, by using separate layers, you can select what is shown at any one time.
You can have more than one page in a Visio file. Choose INSERT|PAGE to add a new page. A dialog box will appear allowing you to change the size of the page, the units, the name of the page, etc. You can also change these properties at a later stage using FILE|PAGE SETUP.
A list of pages will appear at the end of the window . Click on a page tab to select that page. Use the arrows to scroll through the list. Right-click on a page tab if you wish to rename the page, delete it etc.
If you need to draw a number of diagrams for a single document then it makes sense to put them on different pages within a single Visio file.
You can create a new stencil to hold shapes that you have drawn yourself and you may wish to use again. These new ‘masters’ can then be used in the same way as existing masters.
To open a new stencil, select FILE|SHAPES|NEW STENCIL (METRIC). A new stencil will appear as shown below with a default name. You can rename the stencil when you save it. Press the Save icon to the right of the stencil name. You can now give it a sensible name and save it.
Note that in the future when you want to use the stencil again you will have to use FILE|SHAPES|OPEN STENCIL to open it.
You will now add a Master to the stencil. A red star beside the stencil name means that it can be edited. If the red star is not there then right-click on the stencil name and select EDIT STENCIL. Right-click on the stencil now and choose NEW MASTER. A dialog box will appear. For practice you will draw a house so put ‘House’ in the Name box and press OK. An icon should appear with the name underneath it.
Right-click on the icon and select EDIT MASTER|EDIT MASTER SHAPE. A new window will be opened where you can draw the shape. Draw a simple house shape. When finished close the window . You will be asked if you want to update the master. Press Yes. The icon should change to a picture of a house. You can now use the new master in the same way as any other one. Save the changes to the stencil. Repeat what you did to get the red star to appear in order to get out of editing mode.
Visio provides a number of stencils for drawing electrical circuits. If when you start Visio you choose the Electrical Engineering Category and the Basic Electrical (Metric) template then a number of stencils will be opened, Fundamental Items, Semiconductor Items and Electron Tubes, Switches and Relays etc. The Fundamental Items stencil contains masters for resistors, capacitors, ground symbols, voltage sources etc.
Note that when you copy these items onto a page they may be small. That doesn’t mean that you should resize them. Making them bigger can lead to difficulties – you are better off leaving them the preset sizes.
Some of these symbols have leads (e.g. the connection from the Ground Symbol below) and some have not (e.g. the Resistor below). You can connect items using the Connector Tool and the connection points.
How can you shorten the length of a lead in a shape copied from a stencil?
If you try and resize the Ground Symbol then the entire shape is resized. If you want to vary the lead length alone then select the shape and use the Line Tool to reposition the end of the lead.
Note that masters in Visio can contain a number of options. Right-click on a resistor for example and a number of options will appear. Select SHOW ALTERNATE SYMBOL and the shape will change to a rectangle – a standard alternative to that shown above. Other symbols are also available that are based on a resistor, e.g. the symbol for a variable resistor.
For another example copy an Inductor symbol onto your drawing. Right-click on it and select CONFIGURE INDUCTOR. A dialog box allows you to select from a large range of inductor types.
You can add values or labels to the components in a circuit diagram. Most symbols are designed to accommodate text. To add a value to a resistor as shown below either select the Text Tool and click on the resistor or simply double-click on the resistor. You can then type the necessary text. Note the yellow control point that then appears when the shape is selected (see below). You can drag this to reposition the text relative to the symbol - if you move the symbol the text will move with it.
Draw the following circuit diagram. It contains a DC Source, Ground Symbol, and resistor (all from the Fundamental Items stencil) and a ‘light-emitting-diode’ (LED) – named ‘Photodiode’ in the Semiconductors… stencil. Check that the connectors are all joined correctly so that moving any item will not break the circuit. Note that ‘4k7’ is a standard way of indicating a resistance of 4.7 kilo ohms.
If your connections are made correctly then it should be an easy matter to rearrange the diagram to look like that shown below. Use the Rotate Right button to rotate the LED – the connections should change automatically.
Visio can be used for accurately drawing 2D vectors and for performing 2D vector calculations. A vector can be specified in different ways relative to orthogonal axes as illustrated below:
In the first case (a) the length of the vector is specified along with an angle. In the second case (b) the components of the vector in the x and y directions are given. In the third case (c) the length of the vector is given along with the ratio of the two components.
Accurate drawing of vectors is possible using the Size & Position Window (choose VIEW|SIZE & POSITION WINDOW). Draw a line for your vector. The length and angle of the vector are among the properties listed in the window. You can change these properties by selecting the current values and typing over them. Note that the values have associated units. You can enter an angle in degrees (by following the value with “deg”) or in radians (by following the value with “rad”).
Draw a set of axes and draw a vector starting at the origin that is 14.35 mm long and makes an angle of 32° with the x-axis. Make the vector thicker than the axes lines and add an arrow and a label as shown below
Note that it can make life easier if you make sure the origin of your axes is located at the bottom left-hand corner of your page (i.e. at (0, 0)).
Now draw a second vector starting at the origin and ending at (-5, 15.3) mm. Note that if the origin is at (0, 0), then you can draw a line and adjust its End X and End Y properties in the Size & Position Window. Add a label as shown:
You can add A and B in a more than one way. Switch on the Glue to Shape Vertices option . Now drag vector A until the start of the line glues to the end of vector B. You should have:
If you didn’t switch on the glue option then it would be difficult to position the vector correctly.
You could also add the two vectors by dragging vector B to the end of vector A. Now draw a third vector between the origin and the end of A as shown below. Make sure that the end point glues to the end of the line. You can now find the length, angle, and the x and y components of C from the Size & Position Window. Note that the length should be 23.2488 mm.
Make a copy of your previous drawing.
Note that B−A is simply (−A) added to B. You can negate A by rotating it through 180 degrees – select it and press twice. Then do the addition as before:
Alternatively you could calculate B−A by simply joining the two vectors as shown below. As you can see, A + C = B and, therefore, C = B – A. How would you calculate A−B using this method?
You’ve seen how to draw vectors where the two components are given or where the length and the angle are given. What about the third situation illustrated above? If you want, for example, to draw the vector shown below, then draw one that has components 2 and 5 in the x and y-directions, respectively, and then simply change the length property to 9.
Returning to the two vectors specified above,
what is the component of B in the direction of A? First make a line perpendicular to A as shown below. This can be done by copying A and rotating the copy through 90°. You can increase the length of the line if necessary by changing the length property.
Now move the line until the end of it snaps to the end of the vector B as shown below.
The component of B in the direction of A is the distance from the origin to the point at which the new dashed line intersects A. Select Snap to Shape Intersections. Draw a new line so that it snaps to these two points. The new line is highlighted in red below. You can get the length from the Size & Position Window (it should be 3.8675 mm).
Now calculate the component of B that is normal (or “perpendicular”) to A. The answer should be 15.6247 mm.
What if a vector is very short (e.g. 2 units long)? If you draw it 2 mm long then it will be very short and you will have problems with the arrow at its end. If you make it 2 m long then it will be too long for your page. An alternative is simply to scale all your vectors (e.g. make it 20 mm by scaling all vectors by a factor of 10).
Note that a vector equation of the form
C = A + B
is equivalent to 2 scalar equations (if the vectors are in two-dimensions). If there are two unknowns in the equation, then both can be found. A trivial example of this is if you know A and B then you can find both scalars that determine C = A+ B.
This can also be used in more complex situations. For example, if C = A+ B, you know C and the lengths of A and B, then you have two scalar unknowns (the angles of A and C) and two scalar equations. You can solve for these two unknowns graphically using Visio.
Let C = 15i + 20j where i and j are the unit vectors in the x and y directions. Draw this vector. You know that the lengths of A and B are 12 and 19 respectively. Because they add together to give C then they can be drawn as shown below
except you don’t know what A and B are, only their lengths.
What you do know is that the end of A must be 12 units from the origin – it must lie on a circle centred at the origin and with a radius of 12 units. Drag a circle from the Basic Shapes menu. If the origin of your axes is at (0, 0) on your page then change both the X and Y properties of the circle to 0. Change the Height to 24 (since the radius should be 12) – the Width will change automatically.
You also know that the start of B must be 19 units from the end of C so copy the first circle, move the copy until its centre is glued to the end of C, and adjust the Height to the correct value. For this particular problem there are two solutions since the end of A (and start of B) must lie on both circles and there are two points that satisfy these conditions. Draw one of the solutions.
Now consider the situation where C = A + B, you know that B is 20 long and makes an angle of 30° with the x-axis, you know that C is in the y-direction, and you know that A is at 120° to the x-axis. Using Visio, find the lengths of A and C. HINT: Use SHAPE|OPERATIONS|TRIM. Your answer should look like that below and C should be 40 units long.
A rocket taking off at an angle to the
vertical experiences a weight force acting vertically downwards of 50000 N and
a thrust force of 100000 N in the direction in which the rocket is pointed. From
Use Visio to solve this problem. The answer you should get is 82.4355°.
If the mass of the rocket is 5000 kg, what is the magnitude of its acceleration?
A person in a motor-boat wishes to reach appoint directly opposite them across a river. The river flows with a velocity of 1 m/s at right angles to the bank. The boat can travel at a speed of 2 m/s in still water. At what angle should the boat be pointed so as to reach the desired point on the opposite bank? You can solve this by thinking in terms of vectors. The velocity of the boat will equal its velocity relative to the water (which you know has a length of 2 m/s), plus the velocity of the water (whose speed and direction is known). You know what direction the boat should be travelling in. What are the unknowns? Use Visio to find the angle at which the boat should be pointed. The answer should be 60° to the bank as shown below.
If the width of the river is 55 metres, how long will it take the boat to reach the opposite bank? (Answer: 28.87 s).
How about a situation where, for a vector, two components in two different directions are given but those directions are not orthogonal? The diagram below shows a vector A. The components of that vector in the a and b directions are the lengths of the two red lines. This diagram should help you understand the procedure described below.
The component of a vector in the direction 75° to the x-axis is 15 and the component of the same vector in the direction 25° to the x-axis is 12. Draw the vector.
Start by drawing lines from the origin of lengths 15 and 12 in the directions specified as shown below.
Now draw lines normal to these and passing through their end-points.
The end of the vector must be at the intersection of these two lines. Draw the vector. Does this make sense?
Draw the vector A = 4i + 5j. Also draw C = 10i − 15j.
The vector B is normal to A (i.e. it is at 90° to it). You also know that the vector D, where D = B + C, is in the j-direction. Find the length of D.
Answer: 6.9731 units.
Note: If you don’t understand any of these hints then be sure to ask.
and then find you need to resize it in one direction, e.g.
then the arc will no longer be circular and you will lose marks.