The vector `veca+vecb` bisects the angle between the non-collinear vectors `vecaandvecb`, if……..

Explanation

To determine the condition under which the vector \( \vec{A} + \vec{B} \) bisects the angle between the non-collinear vectors \( \vec{A} \) and \( \vec{B} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We want to find the condition such that the vector \( \vec{A} + \vec{B} \) bisects the angle between the vectors \( \vec{A} \) and \( \vec{B} \). This means that the angles formed by \( \vec{A} \) and \( \vec{B} \) with \( \vec{A} + \vec{B} \) are equal.

2. **Assume Angles**: Let the angle between \( \vec{A} \) and \( \vec{A} + \vec{B} \) be \( \theta_1 \) and the angle between \( \vec{B} \) and \( \vec{A} + \vec{B} \) be \( \theta_2 \). For \( \vec{A} + \vec{B} \) to bisect the angle, we need \( \theta_1 = \theta_2 \).

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