Let $\vec{a}$ and $\vec{b}$ be two vectors in the plane (or in a vector space). The difference vector or difference $\vec{a}\!-\!\vec{b}$ of $\vec{a}$ and $\vec{b}$ is a vector $\vec{d}$ such that $$\vec{b}+\vec{d} = \vec{a}.$$ Thus we have

(1)

Remark. It is easily seen that the difference $\vec{a}\!-\!\vec{b}$ is same as the sum vector $$\vec{a}\!+\!(-\vec{b})$$ where $-\vec{b}$ is the opposite vector of $\vec{b}$ : it may be represented by the directed line segment from the terminal point of $\vec{b}$ to the initial point of $\vec{b}$ .