The resultant of two vectors ` vec A and vec B` perpendicular to the vector `vec A and its magnitude id equal to half of the magnitude of the vector ` vec B`. Find out the angle between ` vec A and vec B`.

Explanation

To find the angle between the vectors \( \vec{A} \) and \( \vec{B} \), we can follow these steps:

### Step 1: Understand the Problem
We know that the resultant of two vectors \( \vec{A} \) and \( \vec{B} \) is perpendicular to \( \vec{A} \) and its magnitude is equal to half the magnitude of \( \vec{B} \).

### Step 2: Set Up the Vectors
Assume:
- The vector \( \vec{A} \) is along the x-axis.
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