JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Three Dimensional Geometry

The distance of the point

(- 1, 9, - 16)

from the plane

2 x + 3 y - z = 5

measured parallel to the line

\frac{x + 4}{3} = \frac{2 - y}{4} = \frac{z - 3}{12}

(A) $132$
(B)31
(C)26✓ Correct
(D) $202$

Answer: (C)

Solution

Draw the line through

(- 1, 9, - 16)

parallel to the given direction

(3, - 4, 12)

, with points

(3 λ - 1, - 4 λ + 9, 12 λ - 16)

. Substituting into

2 x + 3 y - z = 5

gives

- 18 λ + 41 = 5

, so

λ = 2

and the point where it meets the plane is

(5, 1, 8)

. The distance, measured along this line, is

(5 + 1)^{2} + (1 - 9)^{2} + (8 + 16)^{2} = 36 + 64 + 576 = 676 = 26.

JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Single correct option

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