Cambridge Additional Mathematics

Vectors (Chapter 11) 303

11 LineLhas equation r=

μ

3

¡ 3

¶

+t

μ

2

5

¶

a Locate the point on the line corresponding to t=1.

b Explain why the direction of the line could also be described by

μ

4

10

¶

c Use your answers toaandbto write an alternative vector equation for lineL.

12 A moving particle has coordinates P(x(t),y(t)) where x(t)=¡4+8t and y(t)=3+6t.

The distance units are metres, and t> 0 is the time in seconds. Find the:

a initial position of the particle b position of the particle after 4 seconds

c particle’s velocity vector d speed of the particle.

Review set 11B

1aFind in component form and in unit vector form:

i

¡!

AB ii

¡!

BC iii

¡!

CA

b Which two vectors in a have the same length?

Explain your answer.

c Write the negative vector of

¡!

CA inthreedifferent

ways.

2 If r=

μ

4

1

¶

and s=

μ

¡ 3

2

¶

find:

a jsj b jr+sj c j 2 s¡rj

3 Findkif the following are unit vectors:

a

μ 5

13

k

¶

b

μ

k

¡k

¶

4 If

¡!

PQ=

μ

¡ 4

1

¶

,

¡!

RQ=

μ

¡ 1

2

¶

, and

¡!

RS=

μ

2

¡ 3

¶

, find

¡!

SP.

5 [MN] is the diameter of a circle with centre C.

a Find the coordinates of M.

b Find the radius of the circle.

6 Findmif

μ

3

m

¶

and

μ

¡ 12

¡ 20

¶

are parallel vectors.

AB

C

M

N,(6 -2)

C,(2 1)

4037 Cambridge

cyan magenta yellow black Additional Mathematics

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\CAM4037\CamAdd_11\303CamAdd_11.cdr Friday, 4 April 2014 2:29:34 PM BRIAN