Answer :

Given: point P(3, 5, 12)


To find: length of the perpendicular drawn from the point P from the x-axis


Formula used:


The distance between any two points (a, b, c) and (m, n, o) is given by,



As, y and z coordinate on x-axis are zero


Let point D on x-axis is (x, 0, 0)


Direction cosines of z-axis are (1, 0, 0)


Direction cosines of PD are (3 – x, 5 – 0, 12 – 0) = (3 – x, 5, 12)


Let are two vectors as shown in the figure:



The dot product of perpendicular vectors is always zero


Therefore,


(3 – x) × 1 + 5 × 0 + 12 × 0 = 0


3 – x + 0 + 0 = 0


x = 3


Hence point D(3, 0, 0)


Distance between point P(3, 5, 12) and D(3, 0, 0) is d






= 13


Hence, the distance of the point P from x-axis is 13 units


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