The coordinates of the foot of the perpendicular from the point (1,-2,1) on the plane containing the lines x+1 6 = y-1 7 = z-3 8 and x-1 3 = y-2 5 = z-3 7 , is:

JEE Main 2017 Mathematics question

The coordinates of the foot of the perpendicular from the point on the plane containing the lines and , is:

Answer: (3)

The plane contains both lines, so its normal is perpendicular to both direction vectors:

n = (6,7,8)×(3,5,7) = i(49-40) - j(42-24) + k(30-21) = (9,-18,9) (1,-2,1).

Using the point from the first line, the plane is

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

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Question ID VK-115850