JEE Main 2022 Mathematics question

If the foot of the perpendicular from the point A(−1, 4, 3) on the plane P : 2x + my + nz = 4, is (−2, 7/2, 3/2), then the distance of the point A from the plane P, measured parallel to a line with direction ratios 3, −1, −4, is equal to :

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

Answer: (2)

Solution

The direction of AB (A to the foot B(−2, 7/2, 3/2)) is (−1, −1/2, −3/2) , 1, 3), which is the normal of the plane, so m = 1 and n = 3. The line through A with direction ratios (3, −1, −4) meets the plane

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Question ID VK-035144