Understanding Engineering Mathematics

a

a + b + c + d + e + f + g

b

c

e

f g

d

Figure 11.4Polygon addition of vectors.

A particular example of this isscalar multiplicationof a vector by a scalar – the vector
kais simplyawith its magnitude scaled byk.
Vectors may be subtracted geometrically as shown in Figure 11.5. Thus, we can denote
the vectorb−aby the ‘arrow’ that takes us fromatob,sinceafollowed byb−agives
the same displacement asb.

a

b

b − a

Figure 11.5Subtraction of vectors.

Exercises on 11.3

1. Consider the pentagon below:

D

C

b

c

d

e

a B

A

E

Express

(i) ein terms ofa,b,c,d

(ii)

−→

CE in terms ofe,a,b

(iii)

−→

CE in terms ofcandd

(iv)

−→

EC in terms of

−→

EA and

−→

CA

2. On a two dimensional Cartesian coordinate system,ais the position vector from the
   origin to the point (1, 0),bis the position vector with length 2 at angle 60°(anti-
   clockwise) to the positivex-axis. Describe the vectorb−a.