Difference between Two Vectors

The reverse of a vector. For a vector $\vec a$, its reverse, written $-\vec a$, is the vector with the same magnitude as $\vec a$ but the opposite direction. If $\vec a=\vec{AB}$, then $-\vec a=\vec{BA}$.

Definition of subtraction. For vectors $\vec a,\vec b$, we define $\vec a-\vec b=\vec a+(-\vec b),$ i.e. subtracting $\vec b$ means adding its reverse.

Geometric picture. Let $\vec{OA}=\vec a$ and $\vec{OB}=\vec b$ be adjacent sides of parallelogram $OACB$, so that the diagonal $\vec{OC}=\vec a+\vec b$ (as in the previous section). It turns out the other diagonal of the same parallelogram, $\vec{BA}$, represents $\vec a-\vec b$. So: **if $\vec a,\vec b$ are two adjacent sides of a parallelogram, its two diagonals represent $\vec a+\vec b$ …