A) \[\sqrt{61}\]sq. unit
B) \[\sqrt{59}\]sq. unit
C) \[\sqrt{49}\]sq. unit
D) \[\sqrt{52}\]sq. unit
Correct Answer: B
Solution :
\[\vec{A}=\hat{j}+3\hat{k}\],\[\vec{B}=\hat{i}+2\hat{j}-\hat{k}\] \[\vec{C}=\vec{A}\times \vec{B}\]\[=\left| \,\begin{matrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 0 & 1 & 3 \\ 1 & 2 & -1 \\ \end{matrix}\, \right|\]\[=-7\hat{i}+3\hat{j}-\hat{k}\] Hence area = \[|\vec{C}|=\sqrt{49+9+1}=\sqrt{59}\,sq\,unit\]
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