Question

The coordinates of the foot of the perpendicular from the point P(1, 0, 0) in the line `(x - 1)/2 = (y + 1)/-3 = (z + 10)/8` are ______.

Options

• (3, –4, –2)

• (–3, 4, 2)

• (3, 4, 2)

• None of these

Answer 1

The coordinates of the foot of the perpendicular from the point P(1, 0, 0) in the line `(x - 1)/2 = (y + 1)/-3 = (z + 10)/8` are (3, –4, –2).

Explanation:

`(x - 1)/2 = (y + 1)/-3 = (z + 10)/8` = r

Any, point of line is

M = (2r + 1, – 3r – 1, 8r – 10)

D.r’s of PM: 2r, – 3r – 1, 8r – 10

and d.r’s of given line are 2, – 3, 8

But PM is perpendicular to the line.

∴ 2(2r) – 3(– 3r – 1) + 8(8r – 10) = 0

∴ 77r = 77

∴ r = 1

∴ M = (3, –4, –2)