Perpendiculars are drawn from points on the line x + 2 2 = y + 1 -1 = z 3 to the plane x + y + z = 3. The feet of perpendiculars lie on the line

JEE Advanced 2013 Mathematics question

Perpendiculars are drawn from points on the line to the plane x + y + z = 3. The feet of perpendiculars lie on the line

(A)
(B)
(C)
(D)Correct

Answer: (D)

Solution

The feet form the projection of the line on the plane. Foot of the point (−2, −1, 0): move along the normal (1, 1, 1): with , giving (0, 1, 2). Direction of the projection: remove the normal component of :

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Question ID VK-026172