If a,b and c are non-coplanar vectors, prove that 3a-7b-4c, 3a-2b+c and a+b+2c are coplanar.

Explanation

To prove that the vectors \( \mathbf{3a - 7b - 4c} \), \( \mathbf{3a - 2b + c} \), and \( \mathbf{a + b + 2c} \) are coplanar, we can use the scalar triple product. The vectors are coplanar if the scalar triple product of these vectors is equal to zero.

### Step-by-step Solution:

1. **Define the Vectors**:
Let:
\[
\mathbf{\alpha} = 3\mathbf{a} - 7\mathbf{b} - 4\mathbf{c}
...