Question

The equation of plane which is perpendicular to the plane $5x+3y+6z+8=0$ and which contains the line of intersection of the planes $x+2y+3z-4=0$ and $2x+y-z+5=0$ is

• A. $51x-15y-50z+173=0$
• B. $51x+15y-50z-173=0$
• C. $51x+15y-50z+173=0$
• D. None of these

Answer 1

The correct option is C

$51x+15y-50z+173=0$

The equation of a plane through the line of intersection of the planes $x+2y+3z-4=0$ and $2x+y-z+5=0$ is

$(x+2y+3z-4)+\lambda (2x+y-z+5)=0\Rightarrow x(1+2\lambda )+y(2+\lambda )+z(-\lambda +3)-4+5\lambda =0$

Also, this is perpendicular to the plane $5x+3y+6z+8=0$

$\therefore 5+10\lambda +6+3\lambda +18-6\lambda =0\Rightarrow \lambda =-\frac{29}{7}$

Substituting value of $\lambda$ we get equation of plane as

$51x+15y-50z+173=0$