So, the addition of vectors is associated with the composition of the corresponding translations. It is easy to see that the set off all vectors forms a commutative group for the addition. The opposite vector of vector A B is vector B A corresponding with the inverse translation. The opposite vector of vector A is noted - A . Then the vector Q is defined as r times the vector P .
Orthogonal projection Take an x-axis with origin in O and any vector P .
Say P' is the orthogonal projection of P on x. Then vector P ' is called the vector-projection of P on x. Definition Let x be an axis with P on x. The dot product of two vectors P and Q is defined by P . It can be proved that P .