The value of $m$, such that $\frac{x-4}{1}=\frac{y-2}{1}=\frac{2 z-m}{3}$ lies in the plane $2 x-5 y+2 z=7$,…
The value of $m$, such that $\frac{x-4}{1}=\frac{y-2}{1}=\frac{2 z-m}{3}$ lies in the plane $2 x-5 y+2 z=7$, is
8
10
9
7
Solution
According to the given condition, point $\left(4,2, \frac{\mathrm{~m}}{2}\right)$ lies on the plane $2 x-5 y+2 z=7$.
$\begin{aligned}
& \Rightarrow 2(4)-5(2)+2\left(\frac{\mathrm{~m}}{2}\right)=7 \\
& \Rightarrow \mathrm{~m}=9
\end{aligned}$