If the lines \frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{- k} \textrm{ }\textrm{ } and \textrm{ }\textrm{ } \frac{x - 1}{k} = \frac{y - 4}{2} = \frac{z

Engineering

Mathematics

Equation of Straight Line in 3D

Question

If 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, then k can have :

exactly two values

any value

exactly one value

exactly three values

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If the lines are coplanar

$| \begin{matrix} 2 - 1 & 3 - 4 & 4 - 5 \\ 1 & 1 & - k \\ k & 2 & 1 \end{matrix} | = 0$ or k² + 3k = 0

$\Rightarrow$ k = 0, – 3.

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