Question

State the essential conditions for addition of vectors.

Answer 1

In order to be able to add two vectors, they must be elements of the same vector space. That means both vectors have the same number of components (same cardinality in the case of infinite vectors), and the components are drawn from the same field. That guarantees the sum will be in that vector space as well.

There is a generalization of vectors and matrices called vexels and maxels where the vectors and matrices are considered padded with zeros in every direction which allows the adding of vectors not usually considered in the same space.

Answer 2

The vectors should have same nature. Eg. Force can be added with force only but not with distance.