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OCR A-level Maths Working with vectors

Working with vectors

This page covers the following topics:

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).

Component form of vectors

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.

Resolving vectors

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 βˆ’ a. Note that the position vector from B to A would be a βˆ’ b. The distance between A and B is just the length of any position vector between them.

Position vectors

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A vector of magnitude 50 makes an angle of 20Β° with the x axis. Find the vector equation, stating your answer in column vector notation.

OCR A-level Maths Working with vectors A vector of magnitude 50 makes an angle of 20Β° with the x axis. Find the vector equation, stating your answer in column vector notation.
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2

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

OCR A-level Maths Working with vectors Find a vector opposite to the one shown in the diagram. Give your answer as a row vector rounding each coordinate to integers.
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3

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

OCR A-level Maths Working with vectors Given the vector equation v = 9i + 3j, what is the magnitude of the x component of the vector?
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4

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What is the vertical component of a 75 N force shown in the picture?

OCR A-level Maths Working with vectors What is the vertical component of a 75 N force shown in the picture?
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5

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A spaceship takes off into space. As it flies, it makes an angle of 10Β° with respect to the vertical axis as shown. Assuming the force on the spaceship is constant, how much force is acting in the horizontal direction? Give your answer to 3 significant figures.

OCR A-level Maths Working with vectors A spaceship takes off into space. As it flies, it makes an angle of 10Β° with respect to the vertical axis as shown. Assuming the force on the spaceship is constant, how much force is acting in the horizontal direction? Give your answer to 3 significant figures.
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6

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What is the position vector b for the point B = (0, 4, 10)? Give your answer in Cartesian coordinates.

OCR A-level Maths Working with vectors What is the position vector b for the point B = (0, 4, 10)? Give your answer in Cartesian coordinates.
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7

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What is the position vector from (1, 1, 1) to (3, 7, 8)?

OCR A-level Maths Working with vectors What is the position vector from (1, 1, 1) to (3, 7, 8)?
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8

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Given the point A = (1, 1, 1) and the position vector from B to A is 2i βˆ’ 4j + k, what is the coordinate of B?

OCR A-level Maths Working with vectors Given the point A = (1, 1, 1) and the position vector from B to A is 2i βˆ’ 4j + k, what is the coordinate of B?
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