Let P be the plane passing through the intersection of planes P_1 : x + y + z - 6 = 0 and P_2 : 2x + 3y + 4z + 5 = 0 . If the plane P contains the ori - Mathematics MCQ Mathematics Mock Test - 11 2026 | ExamTest.live

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Let P be the plane passing through the intersection of planes P_{1} : x + y + z - 6 = 0 and P_{2} : 2 x + 3 y + 4 z + 5 = 0 . If the plane P contains the origin, then the equation of the plane P is:

Solution & Step-by-step Explanation

The equation of a plane passing through the intersection of P_{1} and P_{2} is P_{1} + λ P_{2} = 0 : (x + y + z - 6) + λ (2 x + 3 y + 4 z + 5) = 0 Since the plane passes through the origin (0, 0, 0) : (0 + 0 + 0 - 6) + λ (0 + 0 + 0 + 5) = 0 - 6 + 5 λ = 0 ⟹ λ = 6/5 Substitute λ back into the equation: (x + y + z - 6) + \frac{6}{5} (2 x + 3 y + 4 z + 5) = 0 5 (x + y + z - 6) + 6 (2 x + 3 y + 4 z + 5) = 0 5 x + 5 y + 5 z - 30 + 12 x + 18 y + 24 z + 30 = 0 17 x + 23 y + 29 z = 0

Try it yourself before checking the explanation above.

Let P be the plane passing through the intersection of planes P_{1} : x + y + z - 6 = 0 and P_{2} : 2 x + 3 y + 4 z + 5 = 0 . If the plane P contains the origin, then the equation of the plane P is:

17 x - 23 y - 29 z = 0

17 x + 23 y + 29 z = 0

17 x - 23 y + 29 z = 0

17 x + 23 y - 29 z = 0

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