If $\vec{a}, \vec{b}, \vec{c}, \vec{d}$ are the position vectors of A, B, C, D respectively, then ABCD is a parallelogram if and only if

• a$\vec{b}-\vec{a}=\vec{c}-\vec{d}$
• b$\vec{a}+\vec{b}=\vec{c}+\vec{d}$
• c$\vec{b}-\vec{a}=\vec{d}-\vec{c}$
• d$\vec{a}=\vec{b}=\vec{c}=\vec{d}$