Two (geometric) vectors can be added together to form a new vector. The sum is the diagonal of the parallelogram spanned by the two summands.
Algebraically, the computation of the sum of two vectors in coordinate is very easy:
\[ \begin{bmatrix} x_1 \\ y_1 \end{bmatrix} + \begin{bmatrix} x_2 \\ y_2 \end{bmatrix} = \begin{bmatrix} x_1 + x_2 \\ y_1 + y_2 \end{bmatrix} \]