## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Assume that two vectors, $a_1i+b_1j$ and $a_2i+b_2j$ add up to the zero vector, $0i+0j$. This means that the sums of components add up to zero. This means that $a_1=-a_2$ and $b_1=-b_2$. Therefore, if two vectors $\vec{v_1}$ and $\vec{v_2}$ add up to the zero vector, $\vec{v_2}=-\vec{v_1}$. The magnitude of $\vec{v_1}$ and $-\vec{v_1}$ are the same, so no two vecors with unequal magnitudes can add up to zero.