If ` vec a\ a n d\ vec b\ a n d\ vec c` are mutually perpendicular unit vectors, write the value of `| vec a+ vec b+ vec c|dot`

Explanation

To solve the problem, we need to find the magnitude of the vector sum \( \vec{a} + \vec{b} + \vec{c} \), where \( \vec{a} \), \( \vec{b} \), and \( \vec{c} \) are mutually perpendicular unit vectors.

### Step-by-Step Solution:

1. **Understanding the Properties of the Vectors**:
- Since \( \vec{a} \), \( \vec{b} \), and \( \vec{c} \) are mutually perpendicular unit vectors, we know that:
\[
|\vec{a}| = |\vec{b}| = |\vec{c}| = 1
...