The equation of the plane passing through the intersection of planes 2x-y+z=3, 4x-3y+5z=-9 and parallel to the line x+1 2 = y+3 4 = z-3 5 is ….

MHT CET 2026 Mathematics question

The equation of the plane passing through the intersection of planes , and parallel to the line is ….

(A)11x - 3y – 2z - 54 =0Correct
(B)11x + 3y – 2z – 54 = 0
(C)11x – 3y + 2z – 54 = 0
(D)11x – 3y – 2z + 54 = 0

Answer: (A)

Solution

The planes are and . A plane through their line of intersection is : . It is parallel to the line with direction ratios , so its normal is perpendicular to it:

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Question ID VK-097630