Question

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

• A. $28x-17y+9z=0$
• B. $28x+17y+9z=0$
• C. $2x+17y-9z=0$
• D. $2x-y-z=0$

Answer 1

The correct option is A $28x-17y+9z=0$

Any plane through the line of intersection of the planes:

$2x-y=0$ and $3z-y=0$ is given by

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

$2x+(-1-\lambda )y+3z\lambda =0$ is perpendicular to the plane $4x+5y+3z=0$

$\Rightarrow 4.2+(-1-\lambda ).5+\left(3.\lambda \right)(-3)=0$

$8-5-5\lambda -9\lambda =0$

$3-14\lambda =0$

$\lambda =\frac{3}{14}$

Substituting the value $\lambda$ in equation, we get

$2x+y(-1-\frac{3}{14})+\frac{3z}{14}$

$28x-17y+9z=0$

Hence, the correct option is 'A'.