there are three methods of vector addition:- triangle law- it is a geometrical method and does not has any formula. in this law two vectors are placed in such a way that tail of one vector is joint with head of one vector and the resultant vector is obtained by making a vector whose head is joint with free head and its tail is joint with free tail..................
2) parallelogram law- it is an analytical method and it has a formula....... in this method tail/head of 2 vectors is joined together and the resultant lies between them.
3) polygon law- it is used 2 find resultant of three or more vectors..... in a closed figure resultant is zero............
						

							
 
 
The easiest way to learn how vector addition works is to look at it graphically. There are two equivalent ways to add vectors graphically: the tip-to-tail method and theparallelogram method. Both will get you to the same result, but one or the other is more convenient depending on the circumstances.
Tip-to-Tail Method
We can add any two vectors, A and B, by placing the tail of B so that it meets the tip ofA. The sum, A + B, is the vector from the tail of A to the tip of B.


Parallelogram Method
To add A and B using the parallelogram method, place the tail of B so that it meets the tail of A. Take these two vectors to be the first two adjacent sides of a parallelogram, and draw in the remaining two sides. The vector sum, A + B, extends from the tails ofA and B across the diagonal to the opposite corner of the parallelogram. If the vectors are perpendicular and unequal in magnitude, the parallelogram will be a rectangle. If the vectors are perpendicular and equal in magnitude, the parallelogram will be a square.


Adding Perpendicular Vectors
Suppose vector A has a magnitude of 8, and vector B is perpendicular to A with a magnitude of 6. What is the magnitude of A + B? Since vectors A and B are perpendicular, the triangle formed by A, B, and A + B is a right triangle. We can use the Pythagorean Theorem to calculate the magnitude of A + B


Adding Parallel Vectors
If the vectors you want to add are in the same direction, they can be added using simple arithmetic. For example, if you get in your car and drive eight miles east, stop for a break, and then drive six miles east, you will be 8 + 6 = 14 miles east of your origin. If you drive eight miles east and then six miles west, you will end up 8 – 6 = 2 miles east of your origin.


Adding Vectors at Other Angles
When A and B are neither perpendicular nor parallel, it is more difficult to calculate the magnitude of A + B because we can no longer use the Pythagorean Theorem. It is possible to calculate this sum using trigonometry





 
						

							
fomula for parallelogram law [ i.e. to find the magnitude of vector is under root (A)^2+(B)^@ WHICH WILL BE READ AS UNDER ROOT A(SQUARE)+B(SQUARE)]