Let \[\vec{r}=(\vec{a}\times \vec{b})\sin \,x+(\vec{b}\times \vec{c})\cos \,y+2(\vec{c}\times \vec{a})\] where \[\vec{a},\vec{b},\vec{c}\]three non-coplanar vectors are. If \[\vec{r}\] is perpendicular to \[\vec{a}+\vec{b}+\vec{c},\] the minimum value of \[{{x}^{2}}+{{y}^{2}}\] is

Let \[\vec{r}=(\vec{a}\times \vec{b})\sin \,x+(\vec{b}\times \vec{c})\

1.	Let \[\vec{r}=(\vec{a}\times \vec{b})\sin \,x+(\vec{b}\times \vec{c})\cos \,y+2(\vec{c}\times \vec{a})\] where \[\vec{a},\vec{b},\vec{c}\]three non-coplanar vectors are. If \[\vec{r}\] is perpendicular to \[\vec{a}+\vec{b}+\vec{c},\] the minimum value of \[{{x}^{2}}+{{y}^{2}}\] is
A.	\[{{\pi }^{2}}\]
B.	\[\frac{{{\pi }^{2}}}{4}\]
C.	\[\frac{5{{\pi }^{2}}}{4}\]
D.	None of these
Answer» D. None of these

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Let \[\vec{r}=(\vec{a}\times \vec{b})\sin \,x+(\vec{b}\times \vec{c})\cos \,y+2(\vec{c}\times \vec{a})\] where \[\vec{a},\vec{b},\vec{c}\]three non-coplanar vectors are. If \[\vec{r}\] is perpendicular to \[\vec{a}+\vec{b}+\vec{c},\] the minimum value of \[{{x}^{2}}+{{y}^{2}}\] is

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