The vector `veca+vecb` bisects the angle between the vectors `hata and hatb` if (A) `|veca|+|vecb|=0` (B) angle between `veca and vecb` is zero (C) `|veca|=|vecb|=0` (D) none of these

Explanation

To determine when the vector \(\vec{a} + \vec{b}\) bisects the angle between the vectors \(\hat{a}\) and \(\hat{b}\), we can analyze the conditions under which this occurs.

### Step-by-Step Solution:

1. **Understanding Vector Addition**:
The vector \(\vec{a} + \vec{b}\) represents the diagonal of a parallelogram formed by the vectors \(\vec{a}\) and \(\vec{b}\). For \(\vec{a} + \vec{b}\) to bisect the angle between \(\hat{a}\) and \(\hat{b}\), it must create two equal angles with these vectors.

2. **Condition for Angle Bisector**:
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