Question

The equation of the plane passing through the lines $\frac{x-4}{1}=\frac{y-3}{1}=\frac{z-2}{2}$ and $\frac{x-3}{1}=\frac{y-2}{-4}=\frac{z}{5}$ is-

• A. $11x-y-3z=35$
• B. $11x+y-3z=35$
• C. $11x-y+3z=35$
• D. None of these.

Answer 1

The correct option is D None of these.

Normal vector of the plane is given by,
$\overrightarrow{n}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& 1& 2\\ 1& -4& 5\end{array}\right|=9\hat{i}-3\hat{j}-5\hat{k}$
Hence equation of plane is,
$(\overrightarrow{r}-(3\hat{i}+2\hat{j}\left)\right)\cdot \overrightarrow{n}=0$
$\Rightarrow 9x-3y-5z-21=0$