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प्रश्न
The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and the origin is ______.
विकल्प
3x + 2y + z + 1 = 0
3x + 2y + z = 0
2x + 3y + z = 0
x + y + z = 0
MCQ
रिक्त स्थान भरें
उत्तर
The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and the origin is 3x + 2y + z = 0.
Explanation:
The equation of the required plane is (x + 2y + 3z + 4) + λ(4x + 3y + 2z + 1) = 0 ....(i)
The plane passes through origin i. e., (0, 0, 0)
∴ 4 + λ = 0
⇒ λ = -4
Substituting value of λ in equation (i), we get
-15x - 10y - 5z = 0
⇒ 3x + 2y + z = 0
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