Cambridge Additional Mathematics

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Vectors (Chapter 11) 283

NEGATIVE VECTORS


¡!
AB and
¡!
BA have the same length, but they have opposite directions.

We say that

¡!
BA is thenegativeof

¡!
AB, and write

¡!
BA=¡

¡!
AB.

In the diagram we see the vectora=

μ
2
3


and its negative¡a=

μ
¡ 2
¡ 3


.

If a=

μ
a 1
a 2


then ¡a=

μ
¡a 1
¡a 2


.

EXERCISE 11A


Write the illustrated vectors in component form and in unit vector form:
abc

de f

2 Write each vector in unit vector form, and illustrate it using an arrow diagram:

a

μ
3
4


b

μ
2
0


c

μ
2
¡ 5


d

μ
¡ 1
¡ 3


3aFind in component form and in unit vector form:
i

¡!
AB ii

¡!
BA iii

¡!
BC
iv

¡!
DC v

¡!
AC vi

¡!
DE
b Which two vectors inaare equal? Explain your answer.
c Which two vectors in aare negatives? Explain your
answer.

aaand are parallel
and equal in length,
but opposite in direction.

¡

A

B
¡!
AB

¡!
BA

a -a

2

3-3

-2

A B

D C

E

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Y:\HAESE\CAM4037\CamAdd_11\283CamAdd_11.cdr Thursday, 23 January 2014 1:29:51 PM BRIAN

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