A) \[\frac{3}{2}\]
B) 3
C) \[3\sqrt{3}\]
D) 6
Correct Answer: B
Solution :
\[{{(\hat{x}+\hat{y}+\hat{z})}^{2}}\ge 0\] \[\Rightarrow \]\[3+2\Sigma \hat{x},\hat{y}\ge 0\]\[\Rightarrow \]\[2\Sigma \hat{x}.\hat{y}\ge -3\] Now, \[|\hat{x}+\hat{y}{{|}^{2}}+|\hat{y}+\hat{z}{{|}^{2}}+|\hat{z}+\hat{x}{{|}^{2}}\] \[=6+2\Sigma \hat{x}.\hat{y}\ge 6+(-3)\] \[\Rightarrow \]\[|\hat{x}+\hat{y}{{|}^{2}}|\hat{y}+\hat{z}{{|}^{2}}+|\hat{z}+\hat{x}{{|}^{2}}\ge 3\]
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