Question

The equation of the plane passes through the intersection of $p_1$ & $p_2$ and $\perp$er to the plane $x+2y-3z+6=0$ is

• A. $4x+7y+6z-23=0$
• B. $x-5y-3z=23$
• C. $6x-6y-2z=23$
• D. None of these

Answer 1

Answer: (B)

$x-5y-3z=23$

Equation of any plane passing through the intersection of $p_1$ and $p_2$ can be written as

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

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

The above equation is perpendicular to the plane $x+2y-3z+6=0$
$\therefore$ $1(2+\lambda )+2(-3-\lambda )+(-3)(1+\lambda )=0$
$\therefore$ $\lambda =-\frac{7}{4}$Using the value of $\lambda$ in equation (1), we get the required equation as $x-5y-3z-23=0$

Hence, option (b) is correct answer.