If the sum of two unit vectors is a unit vector, prove that the magnitude of their difference is `sqrt(3.)`

Explanation

To prove that the magnitude of the difference of two unit vectors \( \hat{A} \) and \( \hat{B} \) is \( \sqrt{3} \) given that their sum is also a unit vector, we can follow these steps:

### Step-by-Step Solution:

1. **Given Information**:
- Let \( \hat{A} \) and \( \hat{B} \) be two unit vectors.
- We know that \( \hat{A} + \hat{B} = \hat{C} \), where \( \hat{C} \) is also a unit vector.

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