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Time: 3 hours
Level: Introductory
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 Introduction Resource- In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The...
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| | 1: From geometric to component form, and back
- 1.1: Converting to component form Resource
- In some applications of vectors there is a need to move
backwards and forwards between geometric form and component form; we
deal here with how to achieve this.
- 1.2: Converting to geometric form Resource
- You have seen how any vector given in geometric form, in
terms of magnitude and direction, can be written in component form.
You will now see how conversion in the opposite sense...
- 1.3: Summing vectors given in geometric form Resource
- The following activity illustrates how the conversion
processes outlined in the preceding sections may come in useful. If
two vectors are given in geometric form, and their sum...
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| | 2: Displacements and velocities
- 2.1: Bearings Resource
- In the following subsections, we apply the vector ideas
introduced so far to displacements and velocities. The
examples will feature directions referred to points of the compass,
...
- 2.2: Displacements and bearings Resource
- The displacement from a point P to a point
Q is the change of position between the two points, as
described by the displacement vector
- 2.3: Velocity Resource
- Another vector quantity which crops up frequently in
applied mathematics is velocity. In everyday English, the
words ‘speed’ and
‘velocity’ mean much the same as each...
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- 3: Exercises Resource
- A vector a has magnitude
|a| = 7 and direction
θ = −70°.
Calculate the component form of a, giving the components
correct to two decimal places.
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| | References and Acknowledgements | |
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