If `veca,vecb and vecc` are three non-coplannar vectors, then prove that `(|hataxx(hatbxxhatc)|)/sinA=(|hatbxx(hatcxxhata)|)/sinB=(|hatcxx(hataxxhatb)|)/sin C = (prod|hata xx(hatbxx hatc)|)/(| sum hatn_(1) sinalpha cosbeta cosgamma|)`

Explanation

To prove the given condition involving three non-coplanar vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\), we will follow a systematic approach using vector properties and the sine rule.

### Step-by-step Solution:

1. **Understanding the Sine Rule**:
The sine rule states that for any triangle with sides \(a\), \(b\), and \(c\) opposite to angles \(A\), \(B\), and \(C\) respectively:
\[
\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
...