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| Parallelogram Law of Vectors |
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Consider two vectors
as shown in the figure. Vector
is displaced parallel to itself till the tail end of both the vectors touch at a point O. The parallelogram is completed as shown in the figure. Applying the law of triangle of vectors, to the triangle OAC, we have, |
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| The above example can be stated in the following way as the law of parallelogram of vectors - If two vectors, acting simultaneously at a point, can be represented both in magnitude and direction by the two adjacent sides of a parallelogram drawn from a point, then the resultant is represented completely, both in magnitude and direction by the diagonal of the parallelogram passing through the point. |
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In the figure, two vectors
are completely represented by the two sides OA and OB respectively of a parallelogram. Then, according to the law of parallelogram of vectors, the diagonal OC of
the parallelogram will be resultant
 ,
such that  |
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It is also possible to analytically calculate the magnitude and direction of the resultant vector  . |
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| Let q be the
angle between two given vectors
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From c, drop a perpendicular CN on OA produced. In the right angled D ANC, |
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| Also, |
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| ON = OA + AN = P + Q Cos q |
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| Consider the right angled DONC, |
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| Which is the magnitude of the resultant R. |
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| The direction of the resultant is given by the angle b which is determined in the following way |
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| In this case, q = 00 |
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| b = 00 i.e., the resultant vector also points in the direction of the given vector. |
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| In this case, |
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| The resultant acts in the direction of the larger vector |
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