JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Three Dimensional Geometry

The plane which bisects the line joining the points

(4, - 2, 3)

and

(2, 4, - 1)

at right angles also passes through the point:

(A) $(0, - 1, 1)$
(B) $(4, 0, 1)$
(C) $(4, 0, - 1)$ ✓ Correct
(D) $(0, 1, - 1)$

Answer: (C)

Solution

The plane bisects the segment from

(4, - 2, 3)

(2, 4, - 1)

at right angles, so it passes through the midpoint

(3, 1, 1)

with its normal along the segment, direction

(2, - 6, 4)

or, simplified,

(1, - 3, 2)

. Its equation is

(x - 3) - 3 (y - 1) + 2 (z - 1) = 0

, that is

x - 3 y + 2 z - 2 = 0

. Of the candidate points,

(4, 0, - 1)

satisfies it:

4 - 0 - 2 - 2 = 0

JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Single correct option

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