Show that vectors ` vec a ,\ vec b ,\ vec c` are coplanar if ` vec a+ vec b ,\ vec b+ vec c ,\ vec c+ vec a` are coplanar.

Explanation

To show that the vectors \( \vec{a}, \vec{b}, \vec{c} \) are coplanar if the vectors \( \vec{a} + \vec{b}, \vec{b} + \vec{c}, \vec{c} + \vec{a} \) are coplanar, we can use the property of the scalar triple product.

### Step-by-Step Solution:

1. **Understanding Coplanarity**:
Vectors \( \vec{u}, \vec{v}, \vec{w} \) are coplanar if the scalar triple product \( \vec{u} \cdot (\vec{v} \times \vec{w}) = 0 \).

2. **Expressing the Given Vectors**:
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