Answer:
Given, \[\overrightarrow{a}=2\,\hat{i}+\hat{j}+\hat{k}\]and \[\overrightarrow{b}=3\,\hat{i}+\hat{j}+4\hat{k}\] Then, vector area of the parallelogram is given by \[=\hat{i}\,(4-1)-\hat{j}\,(8-3)+\hat{k}\,(2-3)=3\,\hat{i}-5\hat{j}-\hat{k}\] \[\therefore \]Required area of parallelogram \[=\,\,|\overrightarrow{a}\times \overrightarrow{b}|\,\,=\sqrt{{{(3)}^{2}}+{{(-\,5)}^{2}}+{{(-\,1)}^{2}}}\] \[=\sqrt{9+25+1}=\sqrt{35}\,\,sq\,\,units\]
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