Cambridge International Mathematics

EXERCISE 24E.2

1 If a=

μ

2

¡ 3

¶

, b=

μ

3

¡ 1

¶

, c=

μ

¡ 2

¡ 3

¶

find:

a a+b b b+a c b+c d c+b

e a+c f c+a g a+a h b+a+c

2 Given p=

μ

¡ 1

3

¶

, q=

μ

¡ 2

¡ 3

¶

and r=

μ

3

¡ 4

¶

find exactly:

a p¡q b q¡r c p+q¡r d jpj e jq¡rj f jr+qj

3aGiven

¡!

AB=

μ

1

4

¶

and

¡!

AC=

μ

¡ 2

1

¶

, find

¡!

BC.

b Given

¡!

AB=

μ

¡ 3

2

¶

,

¡!

BD=

μ

0

4

¶

and

¡!

CD=

μ

1

¡ 3

¶

, find

¡!

AC:

4 Find the exact magnitude of these vectors:

a

μ

1

4

¶

b

μ

6

0

¶

c

μ

3

¡ 2

¶

d

μ

¡ 1

¡ 5

¶

e

μ

¡ 4

2

¶

f

μ

¡ 12 a

5 a

¶

5 For the following pairs of points, find: i

¡!

AB ii

a A(3,5) and B(1,2) b A(¡ 2 ,1) and B(3,¡ 1 )

c A(3,4) and B(0,0) d A(11,¡5) and B(¡ 1 ,0)

6 Alongside is a hole at Hackers Golf Club.

a Jack tees off from T and his ball finishes at A. Write a vector

to describe the displacement of the ball from T to A.

b He plays his second stroke from A to B. Write a vector to

describe the displacement with this shot.

c By great luck, Jack’s next shot finishes in the hole H. Write

a vector which describes this shot.

d Use vector lengths to find the distance, correct to 3

significant figures, from:

i TtoH ii TtoA

iii AtoB iv BtoH

e Find the sum of all three vectors for the ball travelling from

T to A to B to H. What information does the sum give about

the golf hole?

7 The diagram alongside shows an orienteering course run

by Kahu.

a Write a column vector to describe each leg of the

course.

b Find the sum of all of the vectors.

c What does the sum inbtell us?

A

B

tee, T

green

H

40 m

A

B

C

D

E

F

G

S

swamp

pine

forest

lake

beach

sea

start

the exact distance AB, i.e.,

̄

̄ ̄¡!

AB

̄

̄ ̄

Vectors (Chapter 24) 495

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Y:\HAESE\IGCSE01\IG01_24\495IGCSE01_24.CDR Monday, 27 October 2008 2:27:04 PM PETER