Cambridge Additional Mathematics

(singke) #1
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)

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Y:\HAESE\CAM4037\CamAdd_11\303CamAdd_11.cdr Friday, 4 April 2014 2:29:34 PM BRIAN

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