Geometrical method
To find a + b , shift vector b such that its initial point coincides with the terminal point of vector a. Now, the vector whose initial point coincides with the initial point of vector a , and terminal point coincides with the terminal point of vector b represents (a +b ) as shown in the above figure.
To find (b +a ), shift a such that its initial point coincides with the terminal point b . A vector whose initial point coincides with the initial point of b and terminal point coincides with the terminal point of a represents (b +a ).
Law of Parallelogram of Vectors
The addition of two vectors may also be understood by the law of parallelogram.
According to this law if two vectors P and Q are represented by two adjacent sides of a parallelogram both pointing outwards as shown in the figure below , then the diagonal drawn through the intersection of the two vectors represents the resultant (i.e. vector sum of P and Q). If Q is displacement from position AD to BC by displacing it parallel to itself, this method becomes equivalent to the triangle method.
In case of addition of two vectors by parallelogram method as shown in figure, the magnitude of resultant will be given by,
(AC)2 = (AE)2 + (EC)2
or R2 = (P + Q cos θ)2 (Q sin θ)2
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