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Working with vectors for AQA A-level Maths

This page covers the following topics:

1. Component form of vectors
2. Resolving vectors
3. Position vectors

If given the angle the vector makes with the x or y axis and the magnitude of the vector, we can work out the vector equations using trigonometry (SOHCAHTOA).

Examples of vectors in physics are force (requires a magnitude of the force and the direction), velocity (the speed is the magnitude and you are given the direction). For calculations, it is often easier to resolve these vectors into their x and y components.

Given any 2 points A and B, they have position vectors a and b which are just vectors from the origin to those points. We can also have the position vector from A to B, which is equal to b − a. Note that the position vector from B to A would be a − b. The distance between A and B is just the length of any position vector between them.

1

What is the y component of a vector that has a magnitude of 50 which makes a 20º angle with the x axis?

2

Give the position vector in Cartesian coordinates from the origin to (1, 5, 6).

i + 5j + 6k

3

Find a vector opposite to the one shown in the diagram. Give your answer as a row vector rounding each coordinate to integers.

v = (−7 −4)

4

A force of 60 N acts on a brick at an angle of 30° to the horizontal surface. What is the magnitude of the horizontal force?

30√3 N

5

Given the vector equation v = 9i + 3j, what is the magnitude of the x component of the vector?

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