If ` hat a ,\ hat b` are unit vector such that`\ hat a+ hat b` is a unit vectors, write the value of `| hat a- hat b|dot`

Explanation

To solve the problem, we need to find the value of \(|\hat{a} - \hat{b}|\) given that \(\hat{a}\) and \(\hat{b}\) are unit vectors and \(\hat{a} + \hat{b}\) is also a unit vector.

### Step-by-step Solution:

1. **Understanding the given information:**
- Since \(\hat{a}\) and \(\hat{b}\) are unit vectors, we have:
\[
|\hat{a}| = 1 \quad \text{and} \quad |\hat{b}| = 1
...