Question

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

• A. $28x-17y+9z=0$
• B. $28x+17y+9z=0$
• C. $28x-17y-9z=0$
• D. $7x-3y+z=0$

Answer 1

Answer: (A)

Equation of plane containing the line of intersection of planes is
$(2x-y)+\lambda (y-3z)=0$ ... (i) Also, plane (i) is perpendicular to
$4x+5y-3z-8=0$
$\therefore$ $4(2)+5(\lambda -1)-3(-3\lambda )=0$
$\Rightarrow$ $14\lambda =-3$
$\Rightarrow$ $\lambda =\frac{-3}{14}$
Putting the value of 'k in Eq. (i), we get
$28x-17y+9z=0$ which is the required plane.