A) \[-13\]
B) \[13/9\]
C) \[-13/9\]
D) \[-9/13\]
Correct Answer: C
Solution :
Let \[\vec{a}=2\hat{i}+\hat{j}-\hat{k},\] \[\vec{b}=-\hat{i}+2\hat{j}+\lambda \hat{k}\] and \[\vec{c}=-5\hat{i}+2\hat{j}-\hat{k}\] are coplanar \[\therefore \] \[[\vec{a}\vec{b}\vec{c}]=0\Rightarrow \left| \begin{matrix} 2 & 1 & -1 \\ -1 & 2 & \lambda \\ -5 & 2 & -1 \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[2(-2-2\lambda )-1(1+5\lambda )-1(-2+10)=0\] \[\Rightarrow \] \[-4-4\lambda -1-5\lambda -8=0\] \[\Rightarrow \] \[-9\lambda =13\] \[\Rightarrow \] \[\lambda =\frac{-13}{9}\]You need to login to perform this action.
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