Cambridge Additional Mathematics

284 Vectors (Chapter 11)

4 Write in component form and illustrate using a directed line segment:

a i+2j b ¡i+3j c ¡ 5 j d 4 i¡ 2 j

5 Write down the negative of:

a

μ

1

4

¶

b

μ

¡ 2

3

¶

c

μ

5

¡ 2

¶

d

μ

0

¡ 6

¶

Consider vector a=

μ

2

3

¶

=2i+3j.

Themagnitudeorlengthofais represented byjaj.

By Pythagoras, jaj^2 =2^2 +3^2 =4+9=13

) jaj=

p

13 units fsince jaj> 0 g

If a=

μ

a 1

a 2

¶

=a 1 i+a 2 j, themagnitudeorlengthofais jaj=

p

a 12 +a 22.

Example 2 Self Tutor

If p=

μ

3

¡ 5

¶

and q=2i¡ 5 j, find:

a jpj b jqj

a p=

μ

3

¡ 5

¶

) jpj=

p

32 +(¡5)^2

=

p

34 units

b q=2i¡ 5 j=

μ

2

¡ 5

¶

) jqj=

p

22 +(¡5)^2

=

p

29 units

UNIT VECTORS

Aunit vectoris any vector which has a length of one unit.

i=

μ

1

0

¶

and j=

μ

0

1

¶

are the base unit vectors in the positive

xandy-directions respectively.

B The magnitude of a vector

2

a 3

cyan magenta yellow black

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_11\284CamAdd_11.cdr Thursday, 23 January 2014 1:30:09 PM BRIAN