If ` vec a\ a n d\ vec b` are two unit vectors such that ` vec a+ vec b` is also a unit vector then find the angle between ` vec a\ a n d\ vec bdot`

Explanation

To solve the problem, we need to find the angle between the two unit vectors \( \vec{a} \) and \( \vec{b} \) given that \( \vec{a} + \vec{b} \) is also a unit vector.

### Step 1: Understand the properties of unit vectors
Since \( \vec{a} \) and \( \vec{b} \) are unit vectors, we know that:
\[ |\vec{a}| = 1 \quad \text{and} \quad |\vec{b}| = 1 \]

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