This gives x = lr Similarly,
y = mr and z = nr
Thus
x2 + y2 + z2 = r2 (l2 + m 2 + n2)
But
x2 + y2 + z2 = r2
Hence
l2 + m2 + n2 = 1
11 2 2  Direction cosines of a line passing through two points
Since one and only one line passes through two given points, we can determine the
direction cosines of a line passing through the given points P(x1, y1, z1) and Q(x2, y2, z2)
as follows (Fig 11