# Analytic method of vector addition

If two vectors display the results from two adjoining sides 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 the opposite angles, 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 a parallelogram, resultant of $\vec{A}$ 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

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 $\vec{R}$ vector $\vec{A}$ is formed by $\theta$

NOW  , OP = A , PE = BCOS$\theta$

To find the value of QE, in triangle PEQ

Special cases

(1) when both the vector are in the same direction

In this
Again  equation

and

Thus the result of the result $\vec{A}$ is equal to the yoga of both vector $\vec{A}$ and in $\vec{A}$ and $\vec{B}$ same direction

(2) when both vectors are at a right angle to each other

(3) When both the vectors are in the opposite direction

then
Again  equation

Thus the result of the resultant vector $\vec{R}$ 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 both vectors is maximized, then both vectors are in the same direction and this is minimal when they are in the direction

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