Prove that `[ -> a , -> b , -> c+ -> d]=[ -> a , -> b , -> c]+[ -> a , -> b , -> d]`

Explanation

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

### Step-by-Step Solution:

1. **Understanding the Scalar Triple Product**:
The scalar triple product \([ \vec{u}, \vec{v}, \vec{w}]\) is defined as \(\vec{u} \cdot (\vec{v} \times \vec{w})\). This means it gives a scalar value which represents the volume of the parallelepiped formed by the three vectors.

2. **Applying the Definition**:
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