If vectors ` vec A , vec` B` and vec C`have magnitudes `5, 12 and 13 units and ` vec A + vec B =vec C`, find theangle between ` vec B and vec C`.

Explanation

To solve the problem, we need to find the angle between vectors \( \vec{B} \) and \( \vec{C} \) given that \( \vec{A} + \vec{B} = \vec{C} \) and the magnitudes of the vectors are \( |\vec{A}| = 5 \), \( |\vec{B}| = 12 \), and \( |\vec{C}| = 13 \).

### Step-by-Step Solution:

1. **Understand the relationship between the vectors**:
We know that \( \vec{A} + \vec{B} = \vec{C} \). This implies that the vectors \( \vec{A} \), \( \vec{B} \), and \( \vec{C} \) form a triangle.

2. **Use the triangle inequality**:
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