Q. 15

# The length of the

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

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