Let ` vec a\ a n d\ vec b` be two unit vectors and `alpha` be the angle between them, then ` vec a+ vec b` is a unit vectors, if
a.`alpha=pi/4` b. `alpha=pi/3` c. `alpha=(2pi)/3` d. `alpha=pi/2`

Explanation

To determine when the vector \( \vec{a} + \vec{b} \) is a unit vector, we start by using the properties of vectors and the dot product.

### Step-by-step Solution:

1. **Understanding the Problem**:
We have two unit vectors \( \vec{a} \) and \( \vec{b} \) with an angle \( \alpha \) between them. We need to find when \( \vec{a} + \vec{b} \) is also a unit vector.

2. **Magnitude of the Sum of Vectors**:
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