A) \[-\frac{4}{3}\]
B) \[\frac{3}{4}\]
C) \[\frac{4}{3}\]
D) 2
Correct Answer: C
Solution :
Since \[\mathbf{a},\,\mathbf{b}\]and \[\mathbf{c}\]are coplanar vectors. \ \[[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]=0\]Þ \[\left| \,\begin{matrix} 1 & 1 & -1 \\ 2 & 3 & 1 \\ 1 & \alpha & 0 \\ \end{matrix}\, \right|=0\] Þ \[1[0-\alpha ]-1[0-1]-1[2\alpha -3]=0\] Þ \[-3\alpha +4=0\Rightarrow \alpha =\frac{4}{3}\].
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