A) 13
B) \[\sqrt{13}\]
C) 6
D) \[\sqrt{6}\]
Correct Answer: B
Solution :
Here \[\overrightarrow{OA}=\mathbf{i}-\mathbf{j}+2\mathbf{k}\] and \[\overrightarrow{OB}=2\mathbf{i}+\mathbf{j}-\mathbf{k}\] and \[\overrightarrow{OC}=3\mathbf{i}-\mathbf{j}+2\mathbf{k}\] These implies \[\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}=\mathbf{i}+2\mathbf{j}-3\mathbf{k}\] and \[\overrightarrow{AC}=\overrightarrow{OC}-\overrightarrow{OA}=2\mathbf{i}\] Hence required area is given by \[=\frac{1}{2}|\overrightarrow{AB}\times \overrightarrow{AC}|\] \[\overrightarrow{AB}\times \overrightarrow{AC}=\left| \begin{matrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 1 & 2 & -3 \\ 2 & 0 & 0 \\ \end{matrix} \right|=-2(3\mathbf{j}+2\mathbf{k})\] \[\Rightarrow \]Area of triangle \[=\frac{1}{2}\times 2|3\mathbf{j}+2\mathbf{k}|=\sqrt{13}\].You need to login to perform this action.
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