Dot product

The dot product is defined for two vectors X and Y to be:

$X\cdot Y=|X||Y|\cos \theta$

where |x| is the norm and theta is the angle between the vectors.

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 projection of X onto the unit vector Y when the tails of the two vectors are placed at the same point.