Cambridge Additional Mathematics

282 Vectors (Chapter 11)

All vectors in the plane can be described in terms of the base unit vectorsiandj.

For example: a=3i¡j

b=¡ 4 i+3j

THE ZERO VECTOR

Thezero vector, 0 , is a vector of length 0.

It is the only vector with no direction.

In component form, 0 =

μ

0

0

¶

.

When we write the zero vector by hand, we usually write

¡!

0.

VECTOR EQUALITY

Two vectors areequalif they have the same magnitude and direction.

In component form, theirx-components are equalandtheiry-components are equal.

Equal vectors areparalleland in the same direction, and are

equal in length. The arrows that represent them are translations

of one another.

Example 1 Self Tutor

a Write

¡!

OA and

¡!

CB in component form and in unit

vector form.

b Comment on your answers ina.

a

¡!

OA=

μ

3

1

¶

=3i+j

¡!

CB=

μ

3

1

¶

=3i+j

b The vectors

¡!

OA and

¡!

CB are equal.

The position vector of any

point relative to itself, is. 0

j

j

j

• i-i-i-i

b

i

• j

i i

a

a

a

a

x

y

C

B

A

O

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_11\282CamAdd_11.cdr Friday, 4 April 2014 2:07:16 PM BRIAN