Mathematics - Vector Question with Solution | TestHub

$\left|\begin{array}{ccc}{\mathrm{x}}_2-{\mathrm{x}}_1& {\mathrm{y}}_2-{\mathrm{y}}_1& {\mathrm{z}}_2-{\mathrm{z}}_1\\ {\mathrm{l}}_1& {\mathrm{m}}_1& {\mathrm{n}}_1\\ {\mathrm{l}}_2& {\mathrm{m}}_2& {\mathrm{n}}_2\end{array}\right|=0$ $\left|\begin{array}{ccc}1& -1& -1\\ 1& 1& -\mathrm{k}\\ \mathrm{k}& 2& 1\end{array}\right|=0\Rightarrow \left|\begin{array}{ccc}0& 0& -1\\ 2& 1+\mathrm{k}& -\mathrm{k}\\ \mathrm{k}+2& 1& 1\end{array}\right|=0$ ${\mathrm{k}}^2+3{\mathrm{k}}^2=0\Rightarrow \mathrm{k}(\mathrm{k}+3)=0$ or $\mathrm{k}=0$ or $-3$