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

The distance of the point

(7, - 3, - 4)

from the plane passing through the points

(2, - 3, 1), (- 1, 1, - 2)

and

(3, - 4, 2)

is :

(A)4
(B)5
(C) $52$ ✓ Correct
(D) $42$

Answer: (C)

Solution

Two edge vectors of the plane are

(- 3, 4, - 3)

and

(1, - 1, 1)

; their cross product gives the normal

(1, 0, - 1)

, so the plane through

(2, - 3, 1)

x - z - 1 = 0

. The distance from

(7, - 3, - 4)

\frac{∣7 - ( - 4 ) - 1∣}{1 ^{2} + ( - 1 ) ^{2}} = \frac{10}{2} = 52 .

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

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