C

Step 1: Let the magnitude of each vector be \( A \).
Step 2: The formula for the resultant \( R \) of two vectors \( A \) and \( B \) forming an angle \( \theta \) between them is given by: \( R = \sqrt{A^2 + B^2 + 2AB \cos \theta} \).
Step 3: Since the vectors are equal, we have: \( R = \sqrt{A^2 + A^2 + 2A^2 \cos \theta} = \sqrt{2A^2(1 + \cos \theta)} = A \).
Step 4: Squaring both sides, we get: \( 2A^2(1 + \cos \theta) = A^2 \).
Step 5: Dividing by \( A^2 \) (assuming \( A \neq 0 \)), we get: \( 2(1 + \cos \theta) = 1 \).
Step 6: This simplifies to: \( 1 + \cos \theta = \frac{1}{2} \) leading to \( \cos \theta = -\frac{1}{2} \).
Step 7: The angle \( \theta \) corresponding to \( \cos \theta = -\frac{1}{2} \) is \( \theta = 120^{ ext{o}} \) or \( \theta = 240^{ ext{o}} \), but the acute angle is considered.
Therefore, the angle between them is \( 120^{ ext{o}} \).
Thus, the correct answer option is C.