The equation of the plane passing through the intersection of `x + 2y + 3x + 4 = 0 and 4x + 3y + 2z+ 1 = 0` and the origin `(0.0, 0)` is

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`.