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please explain addition of vector. of hc verma.

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Scalar quantities can be added algebraically. for example, 4 kg of sugar and 3 kg of sugar, when combined together in any way, always give 7 kg of sugar. This is not always there in case of vectors, since they possess directions, also, in addition to the magnitudes.

Following are the some points regarding vector addition:

(a) Addition or composition of vectors means finding the resultant of a number of vectors acting on a body.

(b) The vectors can be added geometrically and not algebraically.

(c) Vectors, whose resultant is to be calculated behave independent of each other. In other words, each vector behaves as if the other vectors were absent.

(d) Vector addition is commutative.

So,\vec{a}+\vec{b} =\vec{b}+\vec{a} 

It means that the law of addition of vectors is independent of the order of vectors.

Graphical Representation of Vector Addition

                         geometrical-method 

To find \vec{a}+\vec{b} , shift  vector \vec{b} such that its initial point coincides with the terminal point of vector \vec{a}. Now, the vector whose initial point coincides with the initial point of vector \vec{a} , and terminal point coincides with the terminal point of vector \vec{b}  represents \vec{a}+\vec{b} as shown in the above figure. 

To find \vec{b}+\vec{a}, shift \vec{a} such that its initial point coincides with the terminal point \vec{b}. A vector whose initial point coincides with the initial point of \vec{b} and terminal point coincides with the terminal point of \vec{a} represents \vec{b}+\vec{a}.

                       addition-of-two-vectors

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