Answer :

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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