A variety of mathematical operations can be performed with and upon vectors. One such operation is the addition of vectors. Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for vector addition of two or more vectors.

For two vectors vec u = (2,5) e vec v = (2,-3) the vector sum can be obtained this way: vec w = (2,5) + (2,-3) hArr vec w = (2+2,5-3) hArr vec w = (4, 2).

Created with GeoGebra by Vitor Nunes

### Interactivity

Try to move the end sides of the vectors vec u and vec v and see what happens to the resultant vec w.

The sum of two or more vectors is called the resultant. The resultant of two vectors can be found using either the parallelogram method or the triangle method.
Parallelogram Method: Draw the vectors so that their initial points coincide. Then draw lines to form a complete parallelogram. The diagonal from the initial point to the opposite vertex of the parallelogram is the resultant.
Triangle Method: Draw the vectors one after another, placing the initial point of each successive vector at the terminal point of the previous vector. Then draw the resultant from the initial point of the first vector to the terminal point of the last vector. This method is also called the head-to-tail method.