A) \[8\sqrt{2}\]
B) \[8\sqrt{3}\]
C) \[8\sqrt{5}\]
D) \[5\sqrt{8}\]
Correct Answer: B
Solution :
\[\overrightarrow{A}\,\times \,\overrightarrow{B}\,=\left| \,\begin{matrix} \hat{i}\,\, & \hat{j}\,\, & {\hat{k}} \\ 3\,\, & 1\,\, & 2 \\ 2\,\,\, & -2\,\,\, & 4 \\ \end{matrix}\, \right|\,\] \[=(1\times 4-2\times -2)\hat{i}+(2\times 2-4\times 3)\hat{j}+(3\times -2-1\times 2)\hat{k}\] \[=8\hat{i}-8\hat{j}-8\hat{k}\] \Magnitude of \[\overrightarrow{\text{A}}\,\times \overrightarrow{\text{B}}\,=\,|\overrightarrow{\text{A}}\times \overrightarrow{\text{B}}|\,=\sqrt{{{(8)}^{2}}+{{(-8)}^{2}}+{{(-8)}^{2}}}\,\] \[=8\sqrt{3}\]
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