Cambridge Additional Mathematics

(singke) #1
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

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_11\282CamAdd_11.cdr Friday, 4 April 2014 2:07:16 PM BRIAN

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