The value of $m$, such that $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-m}{2}$ lies in the plane $2 x-4 y+z=7$, is
The value of $m$, such that $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-m}{2}$ lies in the plane $2 x-4 y+z=7$, is
7
-7
no real value
4
Solution
The line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-\mathrm{k}}{2}$ lies in the plane $2 x-4 y+z=7$.
$\therefore \quad$ the point $(4,2, k)$ lies on the line and hence lies in the plane
$\begin{array}{ll}
\therefore \quad & 2(4)-4(2)+k=7 \\
& \Rightarrow k=7
\end{array}$