JEE Main 2022 Mathematics question

Let the foot of the perpendicular from the point (1, 2, 4) on the line (x + 2)/4 = (y − 1)/2 = (z + 1)/3 be P. Then the distance of P from the plane 3x + 4y + 12z + 23 = 0 is-

(1)5Correct
(2)50/13
(3)4
(4)63/13

Answer: (1)

Solution

A point on the line is P = (4t − 2, 2t + 1, 3t − 1). The vector from (1, 2, 4) to P is (4t − 3, 2t − 1, 3t − 5), which must be perpendicular to the direction (4, 2, 3):

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Question ID VK-034518