The distance of the point (1,-2,4) from the plane passing through the point (1,2,2) and perpendicular to the planes x-y+2z = 3 and 2x-2y+z+12 = 0, is :

JEE Main 2016 Mathematics question

The distance of the point from the plane passing through the point and perpendicular to the planes and , is :

Answer: (3)

A plane perpendicular to two given planes has its normal perpendicular to both of their normals, so the required normal is the cross product

n = (1,-1,2)×(2,-2,1) = ((-1)(1)-(2)(-2),\ (2)(2)-(1)(1),\ (1)(-2)-(-1)(2)) = (3, 3, 0).

Through the point

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Question ID VK-115582