Cambridge International Mathematics

3 Draw a vector diagram to represent a velocity vector of 50 km/h in a NE direction.

4 An aeroplane is flying in an easterly direction at 300 km/h. It encounters a wind from the north at

20 km/h.

a Draw a vector diagram of the plane’s velocity while being affected by the wind.

b What is the direction of flight during this period?

c How fast is the plane now travelling?

5 Suppose a=

μ

¡ 2

3

¶

, b=

μ

1

4

¶

and c=

μ

¡ 3

¡ 5

¶

.

a Draw a diagram which shows how to find a+b.

b Find: i c+b ii a¡b iii a+b¡c

6 Consider p=

μ

3

2

¶

and q=

μ

¡ 3

¡ 5

¶

.

a Sketch 3 p: b Calculate: i 2 q ii 3 p+2q iii

c Draw a diagram which shows how to find q+2p.

7 Consider the vector m=

μ

2

¡ 5

¶

.

a Illustrate the vector on grid paper. b Find the vector’s length.

c Find the bearing of the vector.

8aFind in component form:

i

¡!

BC ii

¡!

BD

b Simplify

¡!

AD+

¡!

DC:

c Find

¡!

AC.

9 If

μ

¡ 3

¡ 5

¶

and

μ

¡ 6

k

¶

are parallel vectors, findk.

10 If P is(¡ 3 ,2)and Q is(1,¡1), find:

a

¡!

PQ b

̄

̄ ̄¡!

PQ

̄

̄ ̄

:

11 In the figure alongside,

¡!

OA=a,

¡!

OB=b, and

¡!

AC=c.

Find, in terms ofa,bandc:

a

¡!

CA b

¡!

AB c

¡!

OC d

¡!

BC

12 In the given figure

¡!

AD=p and

¡!

AB=2q.

Line segment DC is parallel to line segment AB and is

112 times its length. T is on line segment BC such that

BT : TC=2:1. Find, in terms ofpandq:

a

¡!

DC b

¡!

CB c

¡!

BT

A

B

D C

AC

O

B

a

c

b

p

AB^2 q

DC

T

pq¡ 2

̄

̄ ̄

̄

̄ ̄

502 Vectors (Chapter 24)

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Y:\HAESE\IGCSE01\IG01_24\502IGCSE01_24.CDR Monday, 27 October 2008 2:27:24 PM PETER