A) \[4\sqrt{3}\]
B) \[6\sqrt{3}\]
C) \[12\sqrt{3}\]
D) \[18\sqrt{3}\]
E) \[8\sqrt{3}\]
Correct Answer: C
Solution :
\[[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]=\mathbf{a}.(\mathbf{b}\times \mathbf{c})\]\[=\mathbf{a}.(|\mathbf{b}||\mathbf{c}|\sin \theta \,\mathbf{\hat{n}})\] = \[\mathbf{a}(3\times 4\sin \frac{2\pi }{3}.\mathbf{\hat{n}})\]= \[\mathbf{a}.(12\times \frac{\sqrt{3}}{2}\mathbf{\hat{n}})\] = \[6\sqrt{3}|\mathbf{a}||\mathbf{\hat{n}}|\]= \[6\sqrt{3}\times 2\times 1\Rightarrow 12\sqrt{3}\].
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