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Combining vectors for AQA A-level Maths

This page covers the following topics:

1. Combining vectors

Vectors can be added and subtracted to and from one another by performing the appropriate operations between equivalent components. The vector after these operations are applied is called the resultant vector.

Vectors can be multiplied by a scalar by multiplying each component by the scalar. Geometrically, scalar multiplication increases or decreases the length of the vector by a factor of the scalar, but does not affect the direction of the vector.

Combining vectors

1

Simplify the following expression: (1 4 2) โˆ’ 2(1 1 1) + (4 7 2).

(1 4 2) โˆ’ 2(1 1 1) + (4 7 2) =
= (1 4 2) โˆ’ (2 2 2) + (4 7 2) =
= (3 9 2)

(3 9 2)

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2

Given that the resultant vector when a vector is multiplied by the scalar 3 is 27i + 9j, find the original vector.

3(xi + yj) = 27i + 9j
3x = 27
x = 9
3y = 9
y = 3

9i + 3j

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3

Find the resultant vector when the vectors 3i + 5j and i โˆ’ 3j are added together.

3i + 5j + i โˆ’ 3j = 4i + 2j

4i + 2j

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