Cambridge Additional Mathematics

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

4037 Cambridge

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