Cambridge International Mathematics

5 A, M and B are collinear and M is the midpoint of AB.

If a=

¡!

OA and b=

¡!

OB, show that

¡¡!

OM=^12 a+^12 b.

6 In the given figure, AP : PB=4:3. Deduce a vector equation

for

¡!

OP in terms of a=

¡!

OA and b=

¡!

OB.

7 ABCD is a parallelogram and side DC is extended to E

such that DC=CE.

If

¡!

AD=pand

¡!

AB=q, find in terms ofpandq:

a

¡!

DC b

¡!

DE c

¡!

AC

d

¡!

AE e

¡!

EA f

¡!

BE:

8 In triangle OAB, let

¡!

OA=aand

¡!

OB=b. M and N are the

midpoints of sides OB and AB respectively.

a Find vector expressions for:

i

¡!

BA ii

¡¡!

MN.

b What can be deduced fromaii?

c If O is the origin, find the position vectors of:

i M ii N iii the midpoint of MN.

9 ABCD is a parallelogram and M is the midpoint of side DC.

P is located on line segment AM such that AP : PM=2:1.

a If

¡!

AB=p and

¡!

AD=q, find vector expressions for:

i

¡¡!

DM ii

¡!

AP iii

¡!

DB iv

¡!

DP

b What can be deduced about the points D, P and B?

Review set 24A

#endboxedheading

1 On grid paper draw the vectors:

a a=

μ

¡ 2

3

¶

b b=

μ

1

4

¶

c c=

μ

¡ 3

¡ 5

¶

2 Write in the form

μ

x

y

¶

:

a

b

M

A

O B

a

b

P

A

B

O

4 parts

3 parts

DCE

AB

O

A

B

M N

AB

DC

P

M

d

e

ab

Vectors (Chapter 24) 501

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Y:\HAESE\IGCSE01\IG01_24\501IGCSE01_24.CDR Monday, 27 October 2008 2:27:21 PM PETER