JEE Main 2022 Mathematics question
If the plane P passes through the intersection of two mutually perpendicular planes 2x + ky − 5z = 1 and 3kx − ky + z = 5, k < 3 and intercepts a unit length on positive x-axis, then the intercept made by the plane P on the y-axis is
Answer: (4)
Solution
The planes are perpendicular, so their normals satisfy 2(3k) + k(−k) + (−5)(1) = 0, i.e. , so k = 1 or 5, and k < 3 gives k = 1. The planes are 2x + y − 5z = 1 and 3x − y + z = 5. The plane
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