Subtraction of two vectors

Subtraction has already been introduced above as $\bar a-\bar b=\bar a+(-\bar b)$: to subtract $\bar b$ from

$\bar a$, reverse $\bar b$'s arrow and apply the triangle law. In coordinate form this is simply subtracting

like components. If $\overrightarrow{AB}=\bar a$ and $\overrightarrow{BC}=\bar b$, and $D$ is constructed with

$\overrightarrow{BD}=-\overrightarrow{BC}$, then triangle law in $\triangle ABD$ gives

$\overrightarrow{AD}=\overrightarrow{AB}+\overrightarrow{BD}=\overrightarrow{AB}-\overrightarrow{BC}=\bar a-\bar b$. This picture -- reverse one vector, then add tip-to-tail -- is exactly how $\bar a-\bar b$ is drawn …