If two distinct points Q, R lie on the line of intersection of the planes −x + 2y − z = 0 and 3x − 5y + 2z = 0 and PQ = PR = 18 where the point P is (1, −2, 3), then the area of the triangle PQR is equal to

JEE Main 2022 Mathematics question

If two distinct points Q, R lie on the line of intersection of the planes −x + 2y − z = 0 and 3x − 5y + 2z = 0 and where the point P is (1, −2, 3), then the area of the triangle PQR is equal to

(1)
(2)Correct
(3)
(4)

Answer: (2)

Solution

The line of intersection is x = y = z (its direction is (−1, 2, −1) , −5, 2) = (−1, −1, −1)). Let , , ) be the foot of the perpendicular from P(1, −2, 3): PT·(1, 1, 1) = 0 gives , so $α

See the full step-by-step solution

Create a free account to read the complete working, and practise questions like this in a timed test.

Create a free account

Question ID VK-034970