JEE Main 2022 Mathematics question
Let Q and R be two points on the line (x + 1)/2 = (y + 2)/3 = (z − 1)/2 at a distance from the point P(4, 2, 7). Then the square of the area of the triangle PQR is .
Answer: 153
Solution
Let T(2t − 1, 3t − 2, 2t + 1) be the foot of the perpendicular from P to the line. PT (2, 3, 2): 2(2t − 5) + 3(3t − 4) + 2(2t − 6) = 0, so 17t = 34 and t = 2, T = (3, 4, 5). Then
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