Cambridge International Mathematics

Example 2 Self Tutor

ABCD is a parallelogram in which

¡!

AB=a and

¡!

BC=b.

Find vector expressions for:

a

¡!

BA b

¡!

CB c

¡!

AD d

¡!

CD

a

¡!

BA=¡a fthe negative vector of

¡!

ABg b

¡!

CB=¡b fthe negative vector of

¡!

BCg

c

¡!

AD=b fparallel to and the same length as

¡!

BCg

d

¡!

CD=¡a fparallel to and the same length as

¡!

BAg

EXERCISE 24B

1 State the vectors which are:

a equal in magnitude b parallel

c in the same direction d equal

e negatives of one another.

2 Write in terms of vectorsp,qandr:

a

¡!

AB b

¡!

BA c

¡!

BC

d

¡!

CB e

¡!

CA f

¡!

AC

3 The figure alongside consists of two isosceles triangles with

PQkSR and

¡!

PQ=p,

¡!

PS=q.

Which of the following statements are true?

a

¡!

RS=p b

¡!

QR=q c

¡!

QS=q

d QS=PS e

¡!

PS=¡

¡!

RQ

We have already been operating with vectors without realising it.

Bearing problems are an example of this. The vectors in this case

aredisplacements.

A typical problem could be:

“A girl runs from A in a northerly direction for 3 km and then in a

westerly direction for 2 km to B. How far is she from her starting

point and in what direction?”

We can use trigonometry and Pythagoras’ theorem to answer such

problems as we need to findμandx.

C VECTOR ADDITION [5.2]

a

b

A B

D C

a

b

c

d

e

PQ

SR

q

p

N

S

W E

xkm

2km

3km

A

B

q°

A

B

C

r

p

q

486 Vectors (Chapter 24)

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Y:\HAESE\IGCSE01\IG01_24\486IGCSE01_24.CDR Monday, 27 October 2008 2:26:38 PM PETER