A) 16
B) 9
C) 5
D) 1
Correct Answer: D
Solution :
We have \[V=\left| \begin{matrix} 1 & 1 & 0 \\ 1 & 2\cos ec\alpha & 1 \\ 0 & 1 & 2\cos ec\alpha \\ \end{matrix} \right|\] \[=4\cos e{{c}^{2}}\alpha \,-1-2\cos ec\alpha \] \[=4\left[ \cos e{{c}^{2}}\alpha -\frac{1}{2}\cos ec\,\alpha \right]\,-1=4{{\left( \cos ec\alpha =\frac{1}{4} \right)}^{2}}=\frac{5}{4}\] \[\therefore \,\,{{V}_{least}}\left( \alpha =\frac{\pi }{2} \right)=4\times \frac{9}{16}-\frac{5}{4}=\frac{4}{4}=1\]You need to login to perform this action.
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