Explore the geometrical meaning of vector addition using this interactive tool. Vectors are mathematical quantities used to represent concepts such as force or velocity which have both a magnitude and a direction.
If vectors \( \vec{A} \) and \( \vec{B} \) are given by their components as follows:
\[ \vec{A} = \langle u_1 , v_1 \rangle \quad \text{and} \quad \vec{B} = \langle u_2 , v_2 \rangle \]
then the components of vector \( \vec{A} + \vec{B} \) are given by:
\[ \vec{A} + \vec{B} = \langle u_1 + u_2 , v_1 + v_2 \rangle \]
The parallelogram method shows how vector addition works geometrically: place the tail of vector B at the head of vector A, then draw the vector from the tail of A to the head of B.