Changes

It follows from the above definition that the dot product of X and Y is 0 if X is perpendicular to Y.  

It follows from the above definition that the dot product of X and Y is 0 if X is perpendicular to Y.  

Alternatively, one can describe the dot product as the length of the geometric interpretation of X onto the unit vector Y when the tails of the two vectors are placed at the same point.

Alternatively, one can describe the dot product as the length of the geometric projection of X onto the unit vector Y when the tails of the two vectors are placed at the same point.

[[category:mathematics]]

[[category:mathematics]]

[[category:physics]]

[[category:physics]]