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
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_11\284CamAdd_11.cdr Thursday, 23 January 2014 1:30:09 PM BRIAN