Describing vectors in terms of their components greatly simplifies the vector arithmetic that we described in Section 3-2. Here are the rules: If you add the vectors \(\vec{A}\) and \(\vec{B}\) to form the vector sum \(\vec{C} = \vec{A} + \vec{B}\), each component of \(\vec{C}\) is just the sum of the corresponding components of \(\vec{A}\) and \(\vec{B}\).