If $\vec{A}, \vec{B}, \vec{C}$ are three non coplanar vectors then\ $\frac{\vec{A} \cdot(\vec{B}

Question

If $\vec{A}, \vec{B}, \vec{C}$ are three non coplanar vectors then\ $\frac{\vec{A} \cdot(\vec{B} 	imes \vec{C})}{(\vec{C} 	imes \vec{A}) \cdot \vec{B}}+\frac{\vec{B} \cdot(\vec{A} 	imes \vec{C})}{\vec{C} \cdot(\vec{A} 	imes \vec{B})}=$ $\_\_\_\_$

Professor PC Thomas Classes · Answer

$\frac{\vec{A} \cdot(\vec{B} 	imes \vec{C})}{(\vec{C} 	imes \vec{A}) \cdot \vec{B}}+\frac{\vec{B} \cdot(\vec{A} 	imes \vec{C})}{\vec{C} \cdot(\vec{A} 	imes \vec{B})}=\frac{[\vec{A} \vec{B} \vec{C}]}{[\vec{C} \vec{A} \vec{B}]}+\frac{[\vec{B} \vec{A} \vec{C}]}{[\vec{C} \vec{A} \vec{B}]} =\frac{[\vec{A} \vec{B} \vec{C}]-[\vec{A} \vec{B} \vec{C}]}{[\vec{C} \vec{A} \vec{B}]}=0$