Cambridge Additional Mathematics

288 Vectors (Chapter 11)

Example 7 Self Tutor

If p=3i¡ 5 j and q=¡i¡ 2 j, find jp¡ 2 qj.

p¡ 2 q=3i¡ 5 j¡2(¡i¡ 2 j)

=3i¡ 5 j+2i+4j

=5i¡j

) jp¡ 2 qj=

p

52 +(¡1)^2

=

p

26 units

EXERCISE 11C

1 If a=

μ

¡ 3

2

¶

, b=

μ

1

4

¶

, and c=

μ

¡ 2

¡ 5

¶

find:

a a+b b b+a c b+c d c+b

e a+c f c+a g a+a h b+a+c

2 Given p=

μ

¡ 4

2

¶

, q=

μ

¡ 1

¡ 5

¶

, and r=

μ

3

¡ 2

¶

find:

a p¡q b q¡r c p+q¡r

d p¡q¡r e q¡r¡p f r+q¡p

3 Consider a=

μ

a 1

a 2

¶

.

a Use vector addition to show that a+ 0 =a.

b Use vector subtraction to show that a¡a= 0.

4 For p=

μ

1

5

¶

, q=

μ

¡ 2

4

¶

, and r=

μ

¡ 3

¡ 1

¶

find:

a ¡ 3 p b^12 q c 2 p+q d p¡ 2 q

e p¡^12 r f 2 p+3r g 2 q¡ 3 r h 2 p¡q+^13 r

5 Consider p=

μ

1

1

¶

and q=

μ

2

¡ 1

¶

. Find geometrically and then comment on the results:

a p+p+q+q+q b p+q+p+q+q c q+p+q+p+q

6 For r=

μ

2

3

¶

and s=

μ

¡ 1

4

¶

find:

a jrj b jsj c jr+sj d jr¡sj e js¡ 2 rj

7 If p=

μ

1

3

¶

and q=

μ

¡ 2

4

¶

find:

a jpj b j 2 pj c j¡ 2 pj d j 3 pj e j¡ 3 pj

f jqj g j 4 qj h j¡ 4 qj i

̄

̄^1

2 q

̄

̄ j

̄

̄¡^1

2 q

̄

̄

VECTOR RACE

GAME

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_11\288CamAdd_11.cdr Monday, 6 January 2014 9:55:44 AM BRIAN