Two vectors `vec(A)` and `vec(B)` have precisely equal magnitudes. For the magnitude of `vec(A)`+`vec(B)` to be larger than the magnitude of `vec(A)-vec(B)` by a factor of `n`, what must be the angle between them?

Explanation

To solve the problem, we need to find the angle between two vectors \( \vec{A} \) and \( \vec{B} \) that have equal magnitudes, given that the magnitude of \( \vec{A} + \vec{B} \) is larger than the magnitude of \( \vec{A} - \vec{B} \) by a factor of \( n \).

### Step-by-Step Solution:

1. **Define the Magnitudes**:
Let the magnitude of both vectors be \( A \) (i.e., \( |\vec{A}| = |\vec{B}| = A \)).

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