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 ?
Looks like the range is -1.0 ... 0.0 ... 1.0
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 au is a unit vector pointing in any direction
The angle between two unit vectors:
au · bu = 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).
(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 ?