Parallelogram law of vectors addition

Parallelogram Law of Vector Addition:

This law is also very similar to the triangle law of vector addition. Consider the two vectors again.
Now for using the parallelogram law, we represent both the vectors as adjacent sides of a parallelogram and then the diagonal emanating from the common point represents the sum or the resultant of the two vectors and the direction of the diagonal gives the direction of the resultant vector.

The resultant vector is shown by C. This is known as the parallelogram law of vector addition.

By using the orthogonal system of vector representation the sum of two vectors

a = a₁i^+a₂j^+a₃k^ and b = b₁i^+b₂j^+b₃k^ is given by adding the components of the three axes separately.

i.e. a + b = a_ii^+a₂j^+a₃k^+b₁i^+b₂j^+b₃k^

⇒a+b = (a₁+b₁)i^+(a₂+b₂)j^+(a₃+b₃)k^