2D vectors for OCR GCSE Maths

2D vectors

This page covers the following topics:

1. Adding 2D vectors
2. Subtracting 2D vectors
3. Multiplying 2D vectors
4. Proof with 2D vectors

2D vectors are added by adding their corresponding coordinates or by connecting them “head to toe”.

Adding 2D vectors

To subtract 2D vectors, reverse the direction of the vector that is subtracted or subtract corresponding coordinates.

Subtracting 2D vectors

Two vectors can be multiplied by using a dot product, which can be obtained by multiplying corresponding coordinates and adding the results up. Alternatively, cosine value of an angle between the vectors may be used.

Multiplying 2D vectors

If vectors are multiples of each other, they are parallel to each other.

Proof with 2D vectors

1

Find a − b if a = 4i + 7j and b = 3i − 2j.

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i + 9j

Find a − b if a = 4i + 7j and b = 3i − 2j.

2

P is a point on AB such that AP : PB = 1 : 4. Find OP.

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OP = 0.8a + 0.2b

P is a point on AB such that AP : PB = 1 : 4. Find OP.

3

Find the magnitude of the vector u if u = (2 6).

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2√10

Find the magnitude of the vector u if u = (2 6).

4

Find the direction of (1, 3). Give your answer in 2 decimal places.

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71.57º

Find the direction of (1, 3). Give your answer in 2 decimal places.

5

Obtain the Cartesian expression for this vector, assuming that moving right by one box is i ̂and moving up by one box is j ̂.

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−4i ̂ + 2j ̂

Obtain the Cartesian expression for this vector, assuming that moving right by one box is i ̂and moving up by one box is j ̂.

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