If the lines $\overrightarrow r=(\hat i-\hat j+\hat k)+\lambda(2\hat i+3\hat j+4\hat k)\:\:and\:\:\overrightarrow r=(3\hat i+k\hat j)+\mu(\hat i+2\hat j+\hat k)$ intersect then $k=?$

Question

$\begin{array}{1 1} -1 \\ \frac{2}{9} \\\frac{9}{2} \\ 0 \end{array} $