A) \[-\,1/2\]
B) 1/2
C) 1
D) none of these
Correct Answer: A
Solution :
[a] A vector perpendicular to the plane of O, P and Q is \[\overrightarrow{OP}\times \overrightarrow{OQ}.\] Now, \[\overrightarrow{OP}\times \overrightarrow{OQ}=\left| \begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 4 & 1 & \lambda \\ 2 & -1 & \lambda \\ \end{matrix} \right|=2\lambda \hat{i}-2\lambda \hat{j}-6\hat{k}\] Therefore, \[\hat{i}-\hat{j}+6\hat{k}\] is parallel to \[2\lambda \hat{i}-2\lambda \hat{j}-6\hat{k}\] Hence, \[\frac{1}{2\lambda }=\frac{-1}{-2\lambda }=\frac{6}{-6}\] \[\therefore \lambda =-\frac{1}{2}\]You need to login to perform this action.
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