Cambridge International Mathematics

2 If represents a force of 45 Newtons due east, draw a directed line segment

representing a force of:

a 75 N due west b 60 N south west.

3 Draw a scaled arrow diagram representing the following vectors:

a a velocity of 60 km/h in a NE direction

b a momentum of 45 kg m/s in the direction 250 o

c a displacement of 25 km in the direction 055 o

d an aeroplane taking off at an angle of 10 oto the runway at a speed of 90 km/h.

Two vectors areequalif they have the same magnitudeanddirection.

If arrows are used to represent vectors, then equal vectors are

parallelandequal in length.

This means that equal vector arrows are translations of one another.

THE ZERO VECTOR

It is the only vector with no direction.

NEGATIVE VECTORS

Notice that

¡!

AB and

¡!

BA have the same length but

opposite directions.

We say that

¡!

BA is the negative of

¡!

AB and write

¡!

BA=¡

¡!

AB:

Given the vectorashown, we can draw the vector¡a.

aand¡aare parallel, equal in length, but opposite

in direction.

B VECTOR EQUALITY [5.1, 5.2]

a

a

a

then

a

• a

A

B

¡!

AB

¡!

BA

Vectors (Chapter 24) 485

Thezero vector 0, ,is a vector of length. 0

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Y:\HAESE\IGCSE01\IG01_24\485IGCSE01_24.CDR Tuesday, 18 November 2008 12:01:59 PM PETER