The coordinates of the foot of the perpendicular from a point P(6, 7, 8) on the x-axis are

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)