The line through the point $\hat i+3\hat j+2\hat k$ and $\perp$ to the lines $\overrightarrow r=(\hat i+2\hat j-\hat k)+\lambda(2\hat i+\hat j+\hat k)$ and $\overrightarrow r=(2\hat i+6\hat j+\hat k)+\mu (\hat i+2\hat j+3\hat k)$ is ?

Question

$\begin{array}{1 1} (a)\:\overrightarrow r=(\hat i+2\hat j-\hat k)+\beta(-\hat i+5\hat j-3\hat k)\: \:& \:(b)\:\overrightarrow r=(\hat i+3\hat j+2\hat k)+\beta (\hat i-5\hat j+3\hat k) \\ (c)\:\overrightarrow r=(\hat i+3\hat j+2\hat k)+\beta (\hat i+5\hat j+3\hat k)\:\:&\:(d)\:\overrightarrow r=(\hat i+3\hat j+2\hat k)+\beta (-\hat i+5\hat j+3\hat k) \end{array} $