A) \[\lambda =\mu \]
B) \[\lambda +\mu =0\]
C) \[\lambda \ne \mu \]
D) \[\sqrt{\lambda }+\sqrt{\mu }=1\]
Correct Answer: B
Solution :
Line \[{{L}_{1}}\] is parallel to vector \[\overset{\to }{\mathop{{{v}_{1}}}}\,(say)=\left| \begin{matrix} \widehat{i} & \widehat{j} & \widehat{k} \\ 1 & -\sqrt{\lambda } & 0 \\ 0 & (\sqrt{\lambda }-1) & -1 \\ \end{matrix} \right|=(\sqrt{\lambda })\widehat{i}-\widehat{j}+(\sqrt{\lambda }-1)\widehat{k}\] Also, line \[{{L}_{2}}\]is parallel to vector \[\overset{\to }{\mathop{{{v}_{2}}}}\,(say)=\left| \begin{matrix} \widehat{i} & \widehat{j} & \widehat{k} \\ 1 & -\sqrt{\mu } & 0 \\ 0 & 1-\sqrt{\mu } & -1 \\ \end{matrix} \right|=(\sqrt{\mu })\widehat{i}-\widehat{j}+(1-\sqrt{\mu })\widehat{k}\]As, \[{{v}_{1}}.{{v}_{2}}=0\Rightarrow \sqrt{\lambda }+\sqrt{\mu }=0\Rightarrow \lambda =\mu =0\]You need to login to perform this action.
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