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+1=0

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3x+2y+z=0

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2x+3y+z=0

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x+y+z=0

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Solution

The correct option is B 3x+2y+z=0
Equation of plane passing thrugh the intersection of given planes , is
$(x + 2 y + 3 z + 4) + λ (4 x + 3 y + 2 z + 1) = 0$ $\dots (i)$
Plane (i) is passing through origin i.e., (0,0,0)
$∴ 4 + λ = 0 \Rightarrow λ = - 4$
Put the value of $λ$ in (i)
$- 15 x - 10 y - 5 z = 0 \Rightarrow 3 x + 2 y + z = 0$ .

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x + 2 y + 3 z + 4 = 0

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