Equation of plane containing the line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to the plane…
Equation of plane containing the line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to the plane containing the lines $\frac{x}{3}=\frac{y}{4}=\frac{z}{2}$ and $\frac{x}{4}=\frac{y}{2}=\frac{z}{3}$ is
$x+2 y+z=0$
$x+2 y-z=0$
$x-2 y+z=0$
$x-2 y-\mathrm{z}=0$
Solution
Equation of the plane containing $\frac{x}{3}=\frac{y}{4}=\frac{z}{2}$ and $\frac{x}{4}=\frac{y}{2}=\frac{z}{3}$ is
$\begin{aligned}
& \left|\begin{array}{ccc}
x & y & z \\
3 & 4 & 2 \\
4 & 2 & 3
\end{array}\right|=0 \\
& \Rightarrow 8 x-y-10 z=0
\end{aligned}$
Now required plane is perpendicular to this plane.
Consider option (C)
$(8)(1)+(-1)(-2)+(-10)(1)=0$