Answer :

Given: point P(6, 7, 8)


To find: coordinates of the foot of the perpendicular from a 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 (6 – x, 7 – 0, 8 – 0) = (6 – x, 7, 8)


Let are two vectors as shown in the figure:



The dot product of perpendicular vectors is always zero


Therefore,


(6 – x) × 1 + 7 × 0 + 8 × 0 = 0


6 – x + 0 + 0 = 0


x = 6


Hence, coordinates of the foot of the perpendicular i.e. point D(6, 0, 0)

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