Cambridge International Mathematics

We can now check the results ofExample 13algebraically:

Ina, 2 r+s=2

μ

3

2

¶

+

μ

2

¡ 2

¶

=

μ

6

4

¶

+

μ

2

¡ 2

¶

=

μ

8

2

¶

and inb, r¡ 2 s=

μ

3

2

¶

¡ 2

μ

2

¡ 2

¶

=

μ

3

2

¶

¡

μ

4

¡ 4

¶

=

μ

¡ 1

6

¶

Example 14 Self Tutor

Draw sketches of any two vectorspandqsuch that: a p=2q b p=¡^12 q.

Letqbe ab

EXERCISE 24F

1 For r=

μ

2

3

¶

and s=

μ

4

¡ 2

¶

, find geometrically:

a 2 r b ¡ 3 s c^12 r d r¡ 2 s

e 3 r+s f 2 r¡ 3 s g^12 s+r h^12 (2r+s)

2 Check your answers to 1 using component form arithmetic.

3 Draw sketches of any two vectorspandqsuch that:

a p=q b p=¡q c p=3q d p=^34 q e p=¡^32 q

4 For p=

μ

3

1

¶

and q=

μ

¡ 2

3

¶

, find r=

μ

x

y

¶

such that:

a r=p¡ 3 q b p+r=q c q¡ 3 r=2p d p+2r¡q= 0

5 Ifais any vector, prove that jkaj=jkjjaj: Hint: Writeain component form.

Two vectors areparallelif one is a scalar multiple of the other.

If two vectors are parallel then one vector is a scalar multiple of the other.

Ifais parallel tobthen we write akb.

Thus, ² if a=kb for some non-zero scalark, then akb

² if akb there exists a non-zero scalarksuch that a=kb.

G PARALLEL VECTORS [5.1, 5.2]

q q q

p q p

a

b

Vectors (Chapter 24) 497

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Y:\HAESE\IGCSE01\IG01_24\497IGCSE01_24.CDR Monday, 27 October 2008 2:27:10 PM PETER