JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Three Dimensional Geometry

Let P be the plane, passing through the point

(1, - 1, - 5)

and perpendicular to the line joining the points

(4, 1, - 3)

and

(2, 4, 3)

. Then the distance of P from the point

(3, - 2, 2)

(A)6
(B)4
(C)5✓ Correct
(D)7

Answer: (C)

Solution

The line joining

(4, 1, - 3)

and

(2, 4, 3)

has direction

(- 2, 3, 6)

, which is the normal to

P .

Through

(1, - 1, - 5)

the plane is

- 2 (x - 1) + 3 (y + 1) + 6 (z + 5) = 0

, i.e.

2 x - 3 y - 6 z = 35.

The distance of

(3, - 2, 2)

\frac{∣6 + 6 - 12 - 35∣}{4 + 9 + 36} = \frac{35}{7} = 5.

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Single correct option

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