A) 8
B) \[8\sqrt{3}\]
C) \[3\sqrt{8}\]
D) 192
Correct Answer: A
Solution :
Area of parallelogram \[=\overrightarrow{A}\times \overrightarrow{B}\] \[=(\hat{i}+2\hat{j}+3\hat{k})\times (3\hat{i}-2\hat{j}+\hat{k})\] \[=\left| \,\begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 1 & 2 & 3 \\ 3 & -2 & 1 \\ \end{matrix}\, \right|\]\[=(8)\hat{i}+(8)\hat{j}-(8)\hat{k}\] Magnitude \[=\sqrt{64+64+64}\]=\[8\sqrt{3}\]
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