A) 2
B) 1
C) 3
D) \[-1\]
E) 0
Correct Answer: B
Solution :
\[\because \]\[\overrightarrow{a}=2\hat{i}+\hat{j}+4\hat{k},\overrightarrow{b}=4\hat{i}-2\hat{j}+3\hat{k}\] and\[\overrightarrow{c}=2\hat{i}-3\hat{j}-\lambda \hat{k}\] are coplaner. Hence, \[\left| \begin{matrix} 2 & 1 & 4 \\ 4 & -2 & 3 \\ 2 & -3 & -\lambda \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[2(2\lambda +9)-1(-4\lambda -6)+(-12+4)=0\] \[\Rightarrow \] \[4\lambda +18+4\lambda +6-48+16=0\] \[\Rightarrow \] \[8\lambda -8=0\] \[\Rightarrow \] \[\lambda =1\]You need to login to perform this action.
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