Cambridge International Mathematics

4 If A is at(3,4), B is at(¡ 1 ,2), and C is at(2,¡1), find:

a

¡!

OA b

¡!

AB c

¡!

CO d

¡!

BC e

¡!

CA

VECTOR ADDITION

Consider adding vectors a=

μ

a 1

a 2

¶

and b=

μ

b 1

b 2

¶

.

The horizontal step for a+b is a 1 +b 1.

The vertical step for a+b is a 2 +b 2 :

If a=

μ

a 1

a 2

¶

and b=

μ

b 1

b 2

¶

then a+b=

μ

a 1 +b 1

a 2 +b 2

¶

.

Example 10 Self Tutor

If a=

μ

2

5

¶

and b=

μ

1

¡ 3

¶

, find a+b.

Check your answer graphically.

a+b=

μ

2

5

¶

+

μ

1

¡ 3

¶

=

μ

3

2

¶

NEGATIVE VECTORS

Consider the vector a=

μ

5

2

¶

.

Notice that ¡a=

μ

¡ 5

¡ 2

¶

.

In general, if a=

μ

a 1

a 2

¶

then ¡a=

μ

¡a 1

¡a 2

¶

.

a

ab+ b b 2

a 1

b 1

a 2

ab 11 +

ab 22 +

ab+

b

a

Start at the non-

arrow end and

move horizontally

then vertically to

the arrow end.

a

• a
  5

2-2

-5

Vectors (Chapter 24) 493

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Y:\HAESE\IGCSE01\IG01_24\493IGCSE01_24.CDR Monday, 27 October 2008 2:26:58 PM PETER