Cambridge Additional Mathematics

(singke) #1
Vectors (Chapter 11) 285

Example 3 Self Tutor


Findkgiven that

μ
¡^13
k


is a unit vector.

Since

μ
¡^13
k


is a unit vector,

q
(¡^13 )^2 +k^2 =1

)

q
1
9 +k

(^2) =1
)^19 +k^2 =1 fsquaring both sidesg
) k^2 =^89
) k=§
p 8
3


EXERCISE 11B


1 Find the magnitude of:

a

μ
3
4


b

μ
¡ 4
3


c

μ
2
0


d

μ
¡ 2
2


e

μ
0
¡ 3


2 Find the length of:
a i+j b 5 i¡ 12 j c ¡i+4j d 3 i e kj
3 Which of the following are unit vectors?

a

μ
0
¡ 1


b

Ã
¡p^12
p^1
2

!
c

à 2
3
1
3

!
d

Ã
¡^35

¡^45

!
e

à 2
7
¡^57

!

4 Findkfor the unit vectors:

a

μ
0
k


b

μ
k
0


c

μ
k
1


d

μ
k
k


e

μ 1
2
k


5 Given v=

μ
8
p


and jvj=

p
73 units, find the possible values ofp.

VECTOR ADDITION


Consider adding vectors a=

μ
a 1
a 2


and b=

μ
b 1
b 2


Notice that:
² the horizontal step for a+b is a 1 +b 1
² the vertical step for a+b is a 2 +b 2.

If a=

μ
a 1
a 2


and b=

μ
b 1
b 2


then a+b=

μ
a 1 +b 1
a 2 +b 2


C Operations with plane vectors


a

ab+
b b^2

b 1

a 1

a 2

a+ 2 b 2

a+ 1 b 1

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Y:\HAESE\CAM4037\CamAdd_11\285CamAdd_11.cdr Monday, 6 January 2014 1:02:31 PM BRIAN

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