## Angles Between Vectors and Lines

The anglebetween two vectors u and v is given by the equation

Example: Find the angle between the vectorsand

We can use the same formula to find the angle between vectors in two, three or more dimensions:

Example: Find the angle between the vectorsand

To find the angle between two lines we use the same formula. The vectorsandare the tangent vectors, which are easily identifiable since the general equation of a line is given by the equationwhereis a point on the line andis the tangent vector.

Example: Find the angle between the linesand

Takeand

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.