A) 2
B) \[-2\]
C) 3
D) \[-3\]
Correct Answer: D
Solution :
Given planes are \[\overrightarrow{r}.(2\hat{i}+\lambda \hat{j}-3\hat{k})=0\] and \[\overrightarrow{r}.(\lambda \hat{i}-3\hat{j}+\hat{k})=5\] Here, \[{{\overrightarrow{n}}_{1}}=2\hat{i}+\lambda \hat{j}-3\hat{k}\] and \[{{\overrightarrow{n}}_{2}}=\lambda \hat{i}-3\hat{j}+\hat{k}\] Since both of the planes are perpendicular. \[\therefore \] \[{{\overrightarrow{n}}_{1}}.{{\overrightarrow{n}}_{2}}=0\] \[\Rightarrow \] \[2\lambda -3\lambda -3=0\] \[\Rightarrow \] \[\lambda =-3\]
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