Cambridge Additional Mathematics

292 Vectors (Chapter 11)

are parallel vectors of different length.

Two non-zero vectors areparallelif and only if one is a scalar multiple of the other.

Given any non-zero vectoraand non-zero scalark, the vectorkais parallel toa.

² Ifais parallel tob, then there exists

a scalarksuch that a=kb.

² If a=kb for some scalark, then

I ais parallel tob, and

I jaj=jkjjbj.

Example 10 Self Tutor

Findrgiven that a=

μ

¡ 1

r

¶

is parallel to b=

μ

2

¡ 3

¶

Sinceaandbare parallel, a=kb for some scalark.

)

μ

¡ 1

r

¶

=k

μ

2

¡ 3

¶

) ¡1=2k andr=¡ 3 k

) k=¡^12 and hence r=¡3(¡^12 )=^32

UNIT VECTORS

Given a non-zero vectora, its magnitudejajis a scalar quantity.

If we multiplyaby the scalar

1

jaj

, we obtain the parallel vector

1

jaj

a with length 1.

² A unit vector in the direction ofais

1

jaj

a.

² A vector of lengthkin the same direction asais

k

jaj

a.

² A vector of lengthkwhich isparallel toacould be §

k

jaj

a.

E Parallelism

jj

jj

kkis the modulus of ,

whereas is the length

of vector.

a

a

a^2 a Qea

a

b

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_11\292CamAdd_11.cdr Friday, 4 April 2014 2:10:19 PM BRIAN