To add vector quantities algebraically, the approach we use is explained as follows:

There are namely 2 components in a vector vertical component and horizontal component. When vector is graphed, these components can be seen along two axes 'x' and 'y'. When triangle is completed, vector is supposed to be the longest side while horizontal component is assumed as base and vertical component as perpendicular.

Value of cosine function of angle at which vector is inclined multiplied to magnitude of vector gives the component parallel to x – axis and similarly value of cosine function of angle at which vector is inclined multiplied to magnitude of vector gives the component parallel to y – axis.

So, we can write:

Horizontal Component = size of vector * cos (angle),

For evaluating vertical component we use same angle i.e. subtended by vector with x – axis in positive direction. So, we can write:

Vertical Component = size of vector * sin (angle),

We add two components separately to get the resultant vector as follows:

V

_{x}(summation) = V

_{1}+ V

_{2}+ ... + V

_{n}

V

_{y}(summation) = V

_{1}+ V

_{2}+ ... + Vn

Size of resulting vector would be: Size = √ (Vx

^{2}+ Vy

^{2}).