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

3 x + 2 y + z + 1 = 0

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3 x + 2 y + z = 0

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2 x + 3 y + z = 0

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x + y + z = 0

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Solution

The correct option is B $3 x + 2 y + z = 0$
Any point through the intersection of given planes is
$(x + 2 y + 3 z + 4) + λ (4 x + 3 y + 2 z + 1) = 0$
It contains origin, if
$4 + λ = 0 \Rightarrow λ = - 4$
Therefore, equation of plane is
$x + 2 y + 3 z + 4 - 16 x - 12 y - 8 z - 4 = 0$
$\Rightarrow 15 x + 10 y + 5 z = 0$
$\Rightarrow 3 x + 2 y + z = 0$

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The equation of the plane passing through the origin and perpendicular to the line x=2 y=3 z is

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