A) \[\sqrt{72}\]
B) \[\sqrt{73}\]
C) \[\sqrt{74}\]
D) \[\sqrt{75}\]
Correct Answer: D
Solution :
Since, the diagonals of a parallelogram are \[3\hat{i}+\hat{j}-2\hat{k}\] and \[\hat{i}-3\hat{j}+4\hat{k}\,.\] Then the sides of a parallelogram are \[\vec{a}=2\hat{i}-\hat{j}+\hat{k}\] and \[\vec{b}=\hat{i}+2\hat{j}-3\hat{k}\] Now, \[\vec{a}\times \vec{b}=(2\hat{i}-\hat{j}+\hat{k})\times (\hat{i}+2\hat{j}-3\hat{k})\] \[=\hat{i}+7\hat{j}+5\hat{k}\] Area of parallelogram \[=\left| \vec{a}\times \vec{b} \right|=\sqrt{1+49+25}=\sqrt{75}\]
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