Question

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

• A. $k=1$ or $-1$
• B. $k=0$ or $-3$
• C. $k=3$ or $-3$
• D. $k=0$ or-1

Answer 1

Answer: (B)

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