Addition of vector :- electromagnetic fields , review of vector

Explain about addition of vector.

Consider two coplanar vectors as shown in the fig The vectors which lie in the same plane are called coplanar vectors.

Let us find the sum of these two vectors Ā and B

The procedure is to move one of the two vectors parallel to itself at the tip of the other vector. Thus move Ā parallel to itself at the tip of B.

Then join tip of A moved, to the origin. This vector represents resultant which is the addition of the two vectors A and B. This is shown in the Fig. 1.4.2.

Let us denote this resultant as then

It must be remembered that the direction of C is from origin O to the tip of the vector moved.

Another point which can be noticed that if B is moved parallel to itself at the tip of A, we get the same resultant C Thus, the order of the addition is not important. The addition of vectors obeys the commutative law ie. A+B=B+A.

Another method of performing the addition of vectors is the parallelogram rule. Complete the parallelogram as shown in the Fig. 1.4.3. Then the diagonal of the parallelogram represents the addition of two vector.

Once the co-ordinate systems are defined, then the vectors can be expressed in terms of the components along the axes of the co-ordinate system. Then by adding the corresponding components of the vectors, the components of the resultant vector which is the addition of the vectors, can be obtained. This method is explained after the co-ordinate systems are discussed.

The following basic laws of algebra are obeyed by the vectors A, B and C

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