The equation of the plane through the intersection of the planes $x + 2 y + 3 z - 4 = 0$ and $4 x + 3 y + 3 z + 1 = 0$ and passing through the origin is-

17 x + 14 y + 15 z = 0

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7 x + 4 y + z = 0

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x + 14 y + 11 z = 0

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17 x + y + z = 0

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Solution

The correct option is C $17 x + 14 y + 15 z = 0$
Equation of plane passing through intersection of given plane is given by,
$P_{1} + λ P_{2} = 0 \Rightarrow (x + 2 y + 3 z - 4) + λ (4 x + 3 y + 3 z + 1) = 0$
Given it also passes through origin $\Rightarrow - 4 + λ = 0 \Rightarrow λ = 4$
Hence required plane is, $17 x + 14 y + 15 z = 0$

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