QJEEM13Ma1382: JEE Main 2013 Mathematics - Class 12 JEEM13Ma1382 Solution: If the lines and are coplanar, then can have :

Question

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If the lines

{{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}

and

{{x - 1} \over k} = {{y - 4} \over 2} = {{z - 5} \over 1}

are coplanar, then

k

can have :

Accepted Answer

Given lines will be coplanar

If

| \begin{matrix} - 1 & 1 & 1 \\ 1 & 1 & - k \\ k & 2 & 1 \end{matrix} | = 0

\Rightarrow - 1\left( {1 + 2k} \right) - \left( {1 + {k^2}} \right) + 1\left( {2 - k} \right) = 0

\Rightarrow k = 0, - 3

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