The dot product of two vectors
and
is a number. It is the length of the of vector projected onto the unit vector in the direction of
If
is the angle betweenand then from the diagram above
This equation is usually written
or
and this form can be used to find the angle between two vectors.
To find the dot product of two vectors written in component form we multiply corresponding coordinates and add all the answers.
Example: Find the dot product of
and
Written in vector ijk notation this would be
and
The angle between the two vectors is the solution to
