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AQA GCSE Maths 2D vectors

2D vectors

This page covers the following topics:

2D vectors are added by adding their corresponding coordinates or by connecting them β€œhead 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

The magnitude of a 2D vector is found using Pythagoras' theorem for a right angle triangle, given by M = √(a² + b²).

Magnitude of 2D vectors

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

Proof with 2D vectors

1

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Express c in terms of the other vectors.

AQA GCSE Maths 2D vectors Express c in terms of the other vectors.
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2

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Alice is at her house which is at O. She decides to go to the park which is at D. Express her journey as a vector in terms of vectors a and b.

AQA GCSE Maths 2D vectors Alice is at her house which is at O. She decides to go to the park which is at D. Express her journey as a vector in terms of vectors a and b.
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3

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Subtract a from b if a = (15 16) and b = (10 20).

AQA GCSE Maths 2D vectors Subtract a from b if a = (15 16) and b = (10 20).
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4

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

AQA GCSE Maths 2D vectors Find a βˆ’ b if a = 4i + 7j and b = 3i βˆ’ 2j.
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5

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Write vector (1 3) as a column vector.

AQA GCSE Maths 2D vectors Write vector (1 3) as a column vector.
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6

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

AQA GCSE Maths 2D vectors Find the magnitude of the vector u if u = (2 6).
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7

βœ…

Simplify the expression:

AQA GCSE Maths 2D vectors Simplify the expression:
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8

βœ…

A bike is heading North at 20 km/h. 30ΒΊ West of South Wind suddenly starts blowing at 5 km/h. Find the new direction of the bike in regards to North. Round your answer to units.

AQA GCSE Maths 2D vectors A bike is heading North at 20 km/h. 30ΒΊ West of South Wind suddenly starts blowing at 5 km/h. Find the new direction of the bike in regards to North. Round your answer to units.
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9

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Prove that OMN is a straight line.

AQA GCSE Maths 2D vectors Prove that OMN is a straight line.
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10

βœ…

Determine the vectors RS and SR if R = (1, 2) and S = (3, 5).

AQA GCSE Maths 2D vectors Determine the vectors RS and SR if R = (1, 2) and S = (3, 5).
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