Question

The equation of the plane through the intersection of the planes x+y+z=1 and 2x+3y-z+4=0 parallel to x -axis is

• A. y-3z+6=0
• B. 3y-z+6=0
• C. y+3z+6=0
• D. 3y-2z+6=0

Answer 1

The correct option is A y-3z+6=0

The equation of the plane through the intersection of the plane x+y+z=1 and 2x+3y-z+4=0 is
$(x+y+z-1)+\lambda (2x+3y-z+4)=0$
or $(1+2\lambda )x+(1+3\lambda )y+(1-\lambda )z+4\lambda -1=0$
Since the plane parallel to x-axis,
$\therefore 1+2\lambda =0\Rightarrow \lambda =-\frac{1}{2}$
Hence, the required equation will be y - 3z+6=0.