A) \[7,\,\sqrt{69}\]
B) \[6,\,\sqrt{59}\]
C) \[5,\,\sqrt{65}\]
D) \[5,\,\sqrt{55}\]
Correct Answer: A
Solution :
Let \[\vec{a}=2\hat{i}+4\hat{j}-5\hat{k},\,\,\vec{b}=\hat{i}+2\hat{j}+3\hat{k}\] First diagonal \[=\vec{a}+\vec{b}=3\hat{i}+6\hat{j}-2\hat{k}\] Second diagonal \[=\vec{a}-\vec{b}=\hat{i}+2\hat{j}-8\hat{k}\] Length of first diagonal \[=\sqrt{9+36+4}=\sqrt{49}=7\] Length of second diagonal \[=\sqrt{1+4+64}=\sqrt{69}\]
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