Question

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

• A. 3x+2y+z+1=0
• B. 3x+2y+z=0
• C. 2x+3y+z=0
• D. x+y+z=0

Answer 1

The correct option is B 3x+2y+z=0

Equation of plane passing thrugh the intersection of given planes , is
$(x+2y+3z+4)+\lambda (4x+3y+2z+1)=0$ $\cdots \left(i\right)$
Plane (i) is passing through origin i.e., (0,0,0)
$\therefore 4+\lambda =0\Rightarrow \lambda =-4$
Put the value of $\lambda$ in (i)
$-15x-10y-5z=0\Rightarrow 3x+2y+z=0$.