JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Three Dimensional Geometry

The distance of the point

P (4, 6, - 2)

from the line passing through the point

(- 3, 2, 3)

and parallel to a line with direction ratios

3, 3, - 1

is equal to :

(A)3
(B) $6$
(C) $23$
(D) $14$ ✓ Correct

Answer: (D)

Solution

A general point on the line is

M (3 λ - 3, 3 λ + 2, 3 - λ)

, so

P M = (3 λ - 7, 3 λ - 4, 5 - λ)

. Making

P M

perpendicular to the direction

3, 3, - 1

gives

3 (3 λ - 7) + 3 (3 λ - 4) - (5 - λ) = 0

, i.e.

19 λ = 38

, so

λ = 2

and

M = (3, 8, 1)

. The distance is

P M = 1^{2} + (- 2)^{2} + (- 3)^{2} = 14

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Single correct option

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