If `veca,vecbandvecc` are unit vectors such that `veca+vecb+vecc=0`, then the value of `veca.vecb+vecb.vecc+vecc.veca` is

Options

A. 1
B. 3
C. `-(3)/(2)`
D. None of these

Explanation

To solve the problem, we need to find the value of \( \vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a} \) given that \( \vec{a} + \vec{b} + \vec{c} = 0 \) and that \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
Since \( \vec{a}, \vec{b}, \vec{c} \) are unit vectors, we have:
\[
|\vec{a}| = |\vec{b}| = |\vec{c}| = 1
...