A) \[\sqrt{21}\]
B) \[\frac{\sqrt{21}}{2}\]
C) \[2\sqrt{21}\]
D) \[\frac{\sqrt{21}}{4}\]
Correct Answer: B
Solution :
Let \[\mathbf{a}=\mathbf{i}-3\mathbf{j}+2\mathbf{k},\] \[\mathbf{b}=-\mathbf{i}+2\mathbf{j}\] \[\Rightarrow \mathbf{a}\times \mathbf{b}=\left| \begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & -3 & 2 \\ -1 & 2 & 0 \\ \end{matrix} \right|=-4\mathbf{i}-2\mathbf{j}-\mathbf{k}\] Hence area is equal to \[\frac{1}{2}|\mathbf{a}\times \mathbf{b}|\,=\frac{\sqrt{21}}{2}.\]You need to login to perform this action.
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