Cambridge International Mathematics

Review set 24B

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1 On grid paper draw the vectors:

a p=

μ

1

4

¶

b q=

μ

¡ 3

¡ 1

¶

c r=

μ

5

¡ 2

¶

2 Write in the form

μ

x

y

¶

:

3 Draw a vector diagram to represent a displacement of 200 km in a westerly direction.

4 An aeroplane needs to fly due east to get to its destination. In still air it can travel at 400 km/h.

However, a 40 km/h wind is blowing from the south.

a Draw a vector diagram which shows clearly the direction that the aeroplane must head in.

b What will be the actual speed of the aeroplane and its bearing to the nearest degree?

5

a

¡!

LK b

̄

̄ ̄¡LK!

̄

̄ ̄

6 Findngiven that

μ

¡ 2

¡ 3

¶

and

μ

n

9

¶

are parallel vectors.

7 Suppose d=

μ

3

1

¶

and e=

μ

¡ 2

2

¶

.

a Draw a vector diagram to illustrate d¡e. b Find d¡e in component form.

c Find: i 2 e+3d ii 4 d¡ 3 e

8 What results when opposite vectors are added?

9 If

¡!

AB=p and

¡!

BC=q and ABCD is a parallelogram,

find vector expressions for:

a

¡!

CD b

¡¡!

BM c

¡¡!

MD d

¡!

AD

10 Draw a scale diagram of a velocity vector of 5 km/h with a bearing of 315 o.

11 P and Q are the midpoints of sides AB and BC.

Let

¡!

AP=p and

¡!

BQ=q.

a Find vector expressions for:

i

¡!

PB ii

¡!

QC iii

¡!

PQ iv

¡!

AC

b How are

¡!

PQ and

¡!

AC related?

c Copy and complete:

“the line joining the midpoints of two sides of a triangle is ....... to the third side and ....... its

length”.

ab

m

n

A

D

C

B

M

A

B

C

Q

P

If K is(3 1),¡ and L is(2 5), , find:

Vectors (Chapter 24) 503

IGCSE01

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Y:\HAESE\IGCSE01\IG01_24\503IGCSE01_24.CDR Monday, 27 October 2008 2:27:27 PM PETER