C

Step 1: Given that the magnitudes of vectors \( \vec{OA} \) and \( \vec{OB} \) are equal, we can denote them as \( m \).
Step 2: The equation given is \( \vec{OA} + \vec{OB} - \vec{OC} \).
Step 3: Since \( \vec{OA} = m \) and \( \vec{OB} = m \), we can rewrite the equation:
\( \vec{OA} + \vec{OB} = m + m = 2m \). Hence, the equation becomes: \( 2m - \vec{OC} \).
Step 4: Assuming \( \vec{OC} \) keeps the resultant vector in balance, we analyze the direction.
Step 5: The resultant vector direction of \( \vec{OA} + \vec{OB} \) with respect to \( \vec{OC} \) points in the direction of the sum impacted by \( \vec{OC} \). This results in a direction based on both vectors.
Conclusion: The direction of \( \vec{OA} + \vec{OB} - \vec{OC} \) relates directly to the spatial orientation of vectors \( \vec{OA} \) and \( \vec{OB} \) against \( \vec{OC} \). The given combination leads us to answer option \( C \) that reflects this relationship.