Cambridge International Mathematics

de f

2 For points P, Q, R and S, simplify the following vector expressions:

a

¡!

QR+

¡!

RS b

¡!

PS¡

¡!

RS c

¡!

RS+

¡!

SR

d

¡!

RS+

¡!

SP+

¡!

PQ e

¡!

QP¡

¡!

RP+

¡!

RS f

¡!

RS¡

¡!

PS¡

¡!

QP

3 An aeroplane needs to fly due north at a speed of 500 km/h. However, it is affected by a 40 km/h wind

blowing constantly from the west. What direction must it head towards and at what speed?

4 A motorboat wishes to travel NW towards a safe haven before

an electrical storm arrives. In still water the boat can travel

at 30 km/h. However, a strong current is flowing at 10 km/h

from the north east.

a In what direction must the boat head?

b At what speed will the boat be travelling?

When vectors are drawn on a coordinate grid, we can describe them

in terms of their components in thexandydirections.

μ

x

y

¶

is acolumn vectorand is the vector incomponent form.

For example, given

μ

¡ 1

2

¶

we could draw

where ¡ 1 is thex-component orx-step

and 2 is they-component ory-step.

Example 8 Self Tutor

L(¡ 2 ,3) and M(4,1) are two points. Find a

¡!

LM b

¡!

ML.

a Thex-component goes from¡ 2 to 4 , which is+6.

They-component goes from 3 to 1 , which is¡ 2.

)

¡!

LM=

μ

6

¡ 2

¶

b

¡!

ML=

μ

¡ 6

2

¶

E VECTORS IN COMPONENT FORM [5.1 - 5.3]

p

q

p

q

p

q

-1

2

O

y

x

x-component

y-component

O

y

x

L

M

-2 4

3

Vectors (Chapter 24) 491

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Y:\HAESE\IGCSE01\IG01_24\491IGCSE01_24.CDR Monday, 27 October 2008 2:26:52 PM PETER