The angle
between two vectors u and v is given by the equation
Example: Find the angle between the vectors
and
We can use the same formula to find the angle between vectors in two, three or more dimensions:
Example: Find the angle between the vectors
and
To find the angle between two lines we use the same formula. The vectors
and
are the tangent vectors, which are easily identifiable since the general equation of a line is given by the equation
where
is a point on the line and
is the tangent vector.
Example: Find the angle between the lines
and
Take
and
If the equation of the line is in column vector form, the process is almost identical:
then
The required angle is 180-56.51=123.49 degrees.