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# AQA GCSE Maths 2D vectors

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2D vectors are added by adding their corresponding coordinates or by connecting them βhead to toeβ.

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

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.

The magnitude of a 2D vector is found using Pythagoras' theorem for a right angle triangle, given by M = β(aΒ² + bΒ²).

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

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Express c in terms of the other vectors.

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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.

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

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Find a β b if a = 4i + 7j and b = 3i β 2j.

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Write vector (1 3) as a column vector.

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

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Simplify the expression:

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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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Prove that OMN is a straight line.

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

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