Prove that `[ veca+ vecb , vecb+ vecc , vecc+ veca]=2[ veca , vecb , vecc]`.

Explanation

To prove that \([ \vec{a} + \vec{b}, \vec{b} + \vec{c}, \vec{c} + \vec{a}] = 2[\vec{a}, \vec{b}, \vec{c}]\), we will use the properties of the scalar triple product.

### Step-by-Step Solution:

1. **Understanding the Scalar Triple Product**:
The scalar triple product \([ \vec{x}, \vec{y}, \vec{z}] = \vec{x} \cdot (\vec{y} \times \vec{z})\) gives a scalar value that represents the volume of the parallelepiped formed by the vectors \(\vec{x}\), \(\vec{y}\), and \(\vec{z}\).

2. **Expanding the Left-Hand Side**:
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