The equation of the plane through the intersection of the planes `x+2y+3z-4=0n d4x+3y+2z+1=0` and passing through the origin is a. `17 x+14 y+11 z=0` b. `7x+4y+z=0` c. `x+14+11 z=0` d. `17 x+y+z=0`

Options

A. `17x+14y+11z=0`
B. `7x+4y+z=0`
C. `x+14y+11z=0`
D. `17x+y+z=0`

Answer

a

Explanation

Any plane through the given planes is
`" "x+2y+3z-4+lamda(4x+3y + 2z +1)=0`
It passes through `(0, 0, 0)`. Therefore,
`" "-4+lamda=0`
or `" "lamda=4`
Therefore, the required plane is `x+2y+3z+4(4x+3y+2z)=0 or 17x+ 14y+ 11z=0`.