The length of the perpendicular drawn from the point P(a, b, c) from z-axis is
Given: point P(a, b, c)
To find: distance of the point P from the z-axis
Formula used:
The distance between any two points (a, b, c) and (m, n, o) is given by,
As, x and y coordinate on z-axis are zero
Let point D on z-axis is (0, 0, z)
Direction cosines of z-axis are (0, 0, 1)
Direction cosines of PD are (a – 0, b – 0, c – z) = (a, b, c – z)
Let are two vectors as shown in the figure:
The dot product of perpendicular vectors is always zero
Therefore,
⇒ a × 0 + b × 0 + (c – z) × 1 = 0
⇒ 0 + 0 + c – z = 0
⇒ z = c
Hence point D(0, 0, c)
Distance between point P(a, b, c) and D(0, 0, c) is d
Hence, the distance of the point P from z-axis is units