# Analytic method of vector addition

If two vectors display the results from two adjoining side drawn from any point of a parallelogram in the direction of the result, then the result and direction, the parallelogram that is drawn by the diagonal has been drawn from the same point to add the vector Parallel quadratic rules Assuming vector and are bent at opposite angle, they are displayed in the direction of the parallel quadrilateral OPQS in the direction of OPQS and OP and the OS, then according to the rule of parallelogram, resultant of And will be represented by the diagonal OQ in the result and direction. In order to find the result of the resulting , we increase the side OP and pull the vertical QE from the point Q, thus
Like this QPE =
Thus, in the right angled triangle OEQ

NOW

SO

IN Right-angled triangle

OR

So the final equation will be

,  NOW

OP =A , PQ= OS = B , OQ = R ,,    SO

To find out the direction of the resulting , say that the angle of vector is formed by

NOW  , OP = A , PE = BCOS

To find the value of QE, in triangle PEQ

QE = PQsin = Bsin  ,so

Special cases

(1) when both the vector are in same direction

then  = 0
In this
Again  equation

and

Thus the result of result is equal to yoga of both vector and and in and same direction

(2) when the both vector are at right angle to each other

then  ,   in this

(3) When both the vectors are in opposite direction

then
Again  equation

Thus the result of the resultant vector is equal to the difference of the result of both vectors and in the direction of the large vector
It is clear from the above that the result of the result of both vector is maximized, then both vectors are in the same direction and this is minimal when they are in the direction