Vector(^) calculations
265
P1^
8
When you find the vector
represented by the line segment
joining two points, you are in
effect subtracting their position
vectors. If, for example,
P is the point (2, 1) and Q is the
point (3, 5), P
→
Q is 1
4
,^ as^
figure 8.16 shows.
You find this by saying
P→
Q = P→
O + O→
Q = −p + q.
In this case, this givesP
→
Q = –2
1
3
5
1
4
+
=
as expected.
This is an important result:
P→
Q = q − p
where p and q are the position vectors of P and Q.Geometrical figures
It is often useful to be able to express lines in a geometrical figure in terms of
given vectors.aCTIVITY 8.1 The diagram shows a cuboid OABCDEFG. P, Q, R, S and T are the mid-points of
the edges they lie on. The origin is at O and the axes lie along OA, OC and OD, as
shown in figure 8.17.
O
→
A =6
0
0
,
O
→
C =0
5
0
,
O
→
D =0
0
4
y246135(^012345) x
1
4 ))
P(2, 1)
Q(3, 5)
Figure 8.16
D E
*^6
7
)
2 A
C B
5
4
x 3
y
z
Figure 8.17