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  4. The lines (x-2/1)=(y-3/1)=(z-4/-k) and (x-1/k)=(y-4/2)=(z-5/1) are coplanar if

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Q. The lines $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$ and $\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$ are coplanar if

Solution:

Lines are coplanar $\Rightarrow \begin{vmatrix}2-1 & 3-4 & 4-5 \\ 1 & 1 & -k \\ k & 2 & 1\end{vmatrix}=0$
$\Rightarrow k^{2}+3 k=0 $
$\Rightarrow k=0,-3$.