Vector Operations

**Addition of vectors (2 Dimensional)**

-there are two methods in adding series of vectors in 2 dimensional axes. They are the graphical & analytical methods.

**Graphical Method:**

This Method is used to determine the resultant of series of vectors graphically. This method is of two types, the parallelogram method and the polygon method.

*Parallelogram Method*

In this method, if we are going to determine the resultant of the three vectors, A, B & C, take the resulting vectors is added to the third vector which is vector C and the resulting vector is non the Final vector.

Example:

Determine the resultant vector.

2. *Polygon Method*

In this method, we will connect the series of vectors graphically starting from A reference point up to the last vector then the resultant vector is the vector connecting from A reference point to the head of last vector.

Determine the resultant vector of the three vectors.

**Analytical Method**

This method is done through computation and this is of two types

*1. Component Method*

In this method the magnitude of the resultant vector is obtained by the formula

2. *By Sine and Cosine law*

Consider an Oblique triangle CDE with sides c, d and e.

Sine Law:

c/SinC = d/SinD = e/SinE

Cosine Law:

c^2 = d^2 + e^2 – 2de Cos C

d^2 = c^2 + e^2 – 2ce Cos D

e^2 = c^2 + d^2 – 2cd Cos E