Cambridge International Mathematics

(Tina Sui) #1
Consider a bus which is travelling at 100 km/h in a south east
direction.
A good way of representing this situation is to use an arrow
on a scale diagram.
Thelength of the arrowrepresents the size or magnitude of
the velocity and thearrowheadshows the direction of travel.

Scale: 1 cm represents 50 km/h
Consider the vector represented by the line segment from O to A.

² Thisvectorcould be represented by
¡!
OA or a

bold used
in text books

or a.

used by
students
² Themagnitudeorlengthcould be represented by
j

¡!

OAj or OA or jaj or jaj.

For we say that

¡!

AB is the vector whichemanatesfrom A and
terminatesat B, and that

¡!

AB is theposition vectorof B
relative to A.

Example 1 Self Tutor


On a scale diagram, sketch the vector which representsa velocity of:
a 15 m/s in a westerly direction b 40 m/s on a bearing 075 o.

a Scale: 1 cm ́ 10 m/s b Scale: 1 cm ́ 10 m/s

EXERCISE 24A
1 Using a scale of 1 cm represents 10 units, sketch a vector to represent:
a 40 km/h in a SW direction
b 35 m/s in a northerly direction
c a displacement of 25 m in a direction 120 o
d an aeroplane taking off at an angle of 12 oto the runway with a speed of 60 m/s.

DIRECTED LINE SEGMENT REPRESENTATION


[5.1, 5.3]


A


45°

N

WE

S SE

a

O

A

A

B

N

S

W E

N
75° 40 m/s
15 m/s

~

~

484 Vectors (Chapter 24)

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Y:\HAESE\IGCSE01\IG01_24\484IGCSE01_24.CDR Thursday, 20 November 2008 4:01:09 PM PETER

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