Question

The equation of the plane through the line of intersection of the planes $x+y+z-1=0$ and $2x+y-3z+2=0$ passing through the point $(1,1,1),$ is

• A. $x-4z+3=0$
• B. $x-y+z=1$
• C. $x+y+z=3$
• D. $2x-y+z=2$

Answer 1

The correct option is A $x-4z+3=0$

Equation of plane passing through the intensction of $2$ plane is given by

$p_1+\lambda p_2=0$

$\Rightarrow (x+y+z-1)+\lambda (2x+y-3z+2)=0$

$x(2\lambda +1)+y(\lambda +1)+z(1-3\lambda )+(2\lambda -1)=0$

This plane also passes through $(1,1)$ substituting $(1,1,1)$ in the above equation

we get

$x(-1)+y(-1+1)+z(1+3)+(-2-1)=0$

$-x+4z=3$

$x-4z=-3$

$orx-4z+3=0$, which is the required equation of the plane of the plane.