The equations of the line of shortest distance between the lines x+4 4 = y-2 -2 = z-3 0 and x-5 5 = y-3 3 = z0 are

JEE Advanced Mathematics question

The equations of the line of shortest distance between the lines and are

(A)
(B)
(C)Correct
(D)none of these

Answer: (C)

Solution

The first line lies in the plane with direction . The second lies in with direction . Both directions are horizontal, so their common perpendicular is along , i.e. vertical.

General points: and . is vertical exactly when and

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Question ID VK-109841