Formula for the angle between two Vectors

To do better than guessing, notice that in going from the tail to the head of a the vertical distance increases by 4 while the horizontal distance increases by 4 √2.

Hence the tangent of the angle is 4 / (4 √2)   =  1.0/ √2   =  0.7071.

so the angle with the horizontal is arctan( 0.7071 )  =  35.26°. Since b is in the horizontal plane, the angle between the two vectors must be that value.

The formula for the angle θ between two unit vectors is:

a_u · b_u  =  cosθ

To use this formula with non-unit vectors:

1. normalize each vector,
2. compute the dot product,
3. use the arc cos to get the angle.