3 2 Equation of a line passing through two given points
Let ar  and b
r
 be the position vectors of two
points A (x1, y1, z1) and B(x 2, y 2, z2),
respectively that are lying on a line (Fig 11 5) Let rr  be t he position vector of an
arbitrary point P(x, y, z), then P is a point on
the line if and only if AP
r
a
= −
uuur
r
r  and
AB
b
a
=
−
uuur
r
r  are collinear vectors