# Formula for the Angle between Two Vectors

The range is minus one to plus one,
because each dot product in the previous page is:

(1, 0)^{T} **·** ( cos θ, sin θ)^{T} = cos θ

This is true when **a**_{u} is a unit vector
pointing in any direction

**The angle between two unit vectors:**

**a**_{u} · b_{u} = cos θ

... where
θ
is the angle between the two vectors.
This formula automatically includes the fact that the dot product of
perpendicular vectors is zero (because cos 90° is zero).

### QUESTION 7:

(Calculator Problem: ) What is the cosine of the angle between the two unit vectors
(0.7071, 0.7071)^{T} and (0.5, 0.866)^{T} ?