The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and...

Two planes are coplanar if
\left|$\begin{array}{ccc}x_2-x_1 & y_2-y_1 & z_2-z_1 \\ l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2\end{array}$\right|=0
\left|$$\begin{array}{ccc}1 & -1 & -1 \\ 1 & 1 & -k \\ k & 2 & 1\end{array}$$\right|=0$<br />Applying$\mathrm{C}_2 \rightarrow \mathrm{C}_2+\mathrm{C}_1, \mathrm{C}_3 \rightarrow \mathrm{C}_3+\mathrm{C}_1$<br />$\Rightarrow\left|$$\begin{array}{ccc}1 & 0 & 0 \\ 1 & 2 & 1-k \\ k & k+2 & 1+k\end{array}$$\right|=0$<br />$\Rightarrow \quad 1[2+2 k-(k+2)(1-k)]=0$<br />$\Rightarrow \quad 2+2 k-\left(-k^2-k+2\right)=0$<br />$k^2+3 k=0 \Rightarrow k(k+3)=0