23. Vectors and 3D question bank (Maths)

If \( \vec{a}, \vec{b}, \vec{c} \) are three non-coplanar vectors, then  
\[
\frac{\vec{a} \cdot (\vec{b} \times \vec{c})}{\vec{c} \cdot (\vec{a} \times \vec{b})} + \frac{\vec{b} \cdot (\vec{a} \times \vec{c})}{\vec{c} \cdot (\vec{a} \times \vec{b})} =
\]  

If \( \vec{a}, \vec{b}, \vec{c} \) be any three non-coplanar vectors, then  
\[
[\vec{a} + \vec{b} \quad \vec{b} + \vec{c} \quad \vec{c} + \vec{a}] =
\]