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How to Add Vectors Algebraically?

TopVector is a quantity which has magnitude and direction both. In general we use line and an arrow like for a Ray to symbolize a vector when drawn on paper. Vector size is measured starting from tail to its head represented by arrow or in simple words length of Line Segment. Vector always approach in a particular direction. Let us learn how to add vectors algebraically.

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:
Vx (summation) = V1 + V2 + ... + Vn
Vy (summation) = V1 + V2 + ... + Vn
Size of resulting vector would be: Size = √ (Vx2 + Vy2).