Cambridge International Mathematics

8 Find the two values forkfor which v=

μ

k

3

¶

and jvj=5:

9 u=

μ

k

k

¶

and v=

μ

k+2

1

¶

are two vectors.

a Findkgiven that juj=jvj and v 6 =¡u.

b Check your answers by finding juj and jvj using your value(s) ofk.

Numbers such as 1 and¡ 2 are calledscalarsbecause they have size but no direction.

aand¡ 2 aare examples of multiplying a vector by a scalar.

2 ais the short way of writing a+a and ¡ 2 a=(¡a)+(¡a)

For we have and

So, 2 a has the same direction asaand is twice as long asa, and

¡ 2 a is in the opposite direction toaand is twice as long asa.

Example 13 Self Tutor

For r=

μ

3

2

¶

and s=

μ

2

¡ 2

¶

, find a 2 r+s b r¡ 2 s geometrically.

a

So, 2 r+s=

μ

8

2

¶

:

b

So, r¡ 2 s=

μ

¡ 1

6

¶

:

Ifkis a scalar then k

μ

a

b

¶

=

μ

ka

kb

¶

, so each component is multiplied byk.

F SCALAR MULTIPLICATION [5.2]

a a

2 a a - 2 a -a

• a

r

r s

2 rs¡+¡

• s


• s

r

rs¡-¡2

496 Vectors (Chapter 24)

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Y:\HAESE\IGCSE01\IG01_24\496IGCSE01_24.CDR Monday, 27 October 2008 2:27:07 PM PETER