A) all values of k
B) all except one value of k
C) all except two values of X
D) no value of k
Correct Answer: C
Solution :
The three vectors \[(\overrightarrow{a}+2\overrightarrow{b}+3\overrightarrow{c}),(\lambda \overrightarrow{b}+4\overrightarrow{c})\]and\[(2\lambda -1)\overrightarrow{c}\]are coplanar, if \[\left| \begin{matrix} 1 & 2 & 3 \\ 0 & \lambda & 4 \\ 0 & 0 & 2\lambda -1 \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[(2\lambda -1)(\lambda )=0\] \[\Rightarrow \] \[\lambda =0,\frac{1}{2}\] \[\therefore \]These three vectors are non-coplanar for all except two values of\[\lambda \]\[\left( i.e.,0,\frac{1}{2} \right)\].
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