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State the parallelogram law of vector

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 according to this law, if two vectors are acting at a point and at the same time, they are located on the two adjacent sides of a parallelogram in same magnitude and direction, then the diagonal of the parallelogram will be the resultant.
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ADDITION OF VECTORS
 
PARALLELOGRAM LAW OF VECTOR ADDITION
  
Acccording to the parallelogram law of vector addition:
"If two vector quantities are represented by two adjacent sides or a parallelogram
then the diagonal of parallelogram will be equal to the resultant of these two vectors."
 
EXPLANATION
 
  Consider two vectors . Let the vectors have the following orientation
 
  parallelogram of these vectors is :
According to parallelogram law:
MAGNITUDE OF
RESULTANT VECTOR
  
Magintude or resultant vector can be determined by using either sine law or cosine law.
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Parallelogram Law states that if two vectors acting on a body may be represented completely by two adjacent sides of a parallelogram. then their resultant is represented by a diagonal passing through the common point. See the following diagram -

parallelogram law

We can prove it from properties of parallelogram - the line parallel to vector V is equal to vector B and hence the sum or vector A and vector B is R which is the diagonal of the parallelogram.

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The parallelogram law gives the rule for vector addition of vectors  and . The sum  of the vectors is obtained by placing them head to tail and drawing the vector from the free tail to the free head.

Let  denote the norm of a quantity. Then the quantities  and  are said to satisfy the parallelogram law if

If the norm is defined as  , then the law will always hold.

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