Question

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

• A. $y-3z-6=0$
• B. $y-3z+6=0$
• C. $y-z-1=0$
• D. $y-z+1=0$

Answer 1

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

$(x+y+z)=1$

$2x+3y-z\ne 4=0$ and $11$ to $x$ axis

$(x+y+z-1)+\lambda (2x+3y-z-4)=0$

$x(1+2\lambda )+y(1+3\lambda )+z(1-\lambda )+4\lambda -1=0$

$1+2\lambda =0$

$\lambda =-1/2$

$(x+y+z-1)+-1/2(2x+3y-z+4)=0$

$x+y+z-1-x-\frac{3}{2}y+\frac{z}{2}-2=0$

$-1/2+\frac{3}{2}z-3=0$

$y-3z+0$