Let `vecA and vecB` be two non-parallel unit vectors in a plane. If `(alpha vecA + vecB)` bisets the internal angle between `vecA and vecB` then find the value of `alpha`.

Explanation

To find the value of \( \alpha \) such that \( \alpha \vec{A} + \vec{B} \) bisects the internal angle between the non-parallel unit vectors \( \vec{A} \) and \( \vec{B} \), we can follow these steps:

### Step 1: Understand the condition of angle bisector
Since \( \alpha \vec{A} + \vec{B} \) bisects the angle between \( \vec{A} \) and \( \vec{B} \), we can set up the condition that the angles formed by \( \vec{A} \) with \( \alpha \vec{A} + \vec{B} \) and \( \vec{B} \) with \( \alpha \vec{A} + \vec{B} \) are equal.

### Step 2: Use the dot product
The angle bisector condition can be expressed using the dot product:
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