The equation of the plane, passing through the intersection of the planes x+y+z=1 and 2x+3y-z+4=0 and parallel to Y - axis, is

MHT CET 2024 Mathematics question

The equation of the plane, passing through the intersection of the planes and and parallel to Y - axis, is

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

Answer: (C)

Solution

Any plane through the intersection is , i.e. . A plane is parallel to the Y-axis when its normal is perpendicular to , i.e. the coefficient of is zero: . Substituting:

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Question ID VK-099867