Cambridge International AS and A Level Mathematics Pure Mathematics 1

Vector

(^) calculations
P1^
8
When a is given in component form, the components of −a are the same as those
for a but with their signs reversed. So

–

–

23 –

0

11

23

0

11

















=

+

















adding vectors

When vectors are given in component form, they can be added component by

component. This process can be seen geometrically by drawing them on graph

paper, as in the example below.

ExamPlE 8.7 Add the vectors 2 i − 3 j and 3 i + 5 j.

SOlUTION

2 i −   3 j +   3 i +   5 j =   5 i +   2 j

The sum of two (or more) vectors is called the resultant and is usually indicated

by being marked with two arrowheads.

a –a

Figure 8.12

2 i

3 i

3 i + 5j 5 j

5 i + 2j

–3j

2 i – 3j

Figure 8.13