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

x+y+z=0

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17x+14y+11z=0

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7x+4y+z=0

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17x+14y+z=0

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Solution

The correct option is B 17x+14y+11z=0
Equation of plane passing through intersecting the planes x+2y+3z-4 =0 and 4x+3y+2z+1 =0 is, $x + 2 y + 3 z - 4 + λ (4 x + 3 y + 2 z + 1) = 0$
Since it is passing through origin, so $λ = 4$ .
Hence the required equation is 17x +14y +11z=0.

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x + 2 y + 3 z + 4 = 0

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