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

Explanation

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

### Step 1: Understand the given information
We know that both \( \mathbf{A} \) and \( \mathbf{B} \) are unit vectors. Therefore, we have:
\[ |\mathbf{A}| = 1 \quad \text{and} \quad |\mathbf{B}| = 1 \]
Additionally, we know that the sum of these two vectors is also a unit vector:
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