Thelengthormagnitudeof a vector,a, is denoted|a|or just a. The direction ofais
represented by a vector in the same direction, but with unit magnitude, and is denoted by
aˆ. Thus, we may writea=|a|ˆa.
Exercise on 11.2
Consider vectors in a plane, and use a two-dimensional Cartesian coordinate system with
the usual rectangularx-,y-axes. Choosing suitable scales on the axes sketch vectors as
follows:
(i) Three free vectorsa,b,call of the same length 2 units and making
equal angles with the positivex-andy-axes.
(ii) A position vectorrof length 3 units in the north-west direction (posi-
tivey-axis north).Answers
(i)− 2 − 1 0− 2− 3 23 xy1a− 112(^3) b
c
Figure 11(i)
(ii)
− 3 − 2 − 1 0 23 x
y
1
r
1
2
3
Figure 11(ii)