What is the cosine of the angle between the two unit vectors q_u = (0.0, 1)^T and w_u = (-0.5, 0.866)^T ?

A good answer might be:

Again, cos x = 0.866. So it must be that x = arc cos 0.866 = 30°.

Which Side?

Both vectors r_u and w_u gave the answer cos 30, when the dot product was done with q_u, although they lie on either side of q_u.

In two dimensions, there are two unit vectors that are 30° away from a given vector. Both of them will give you the same dot product with the given vector. Be careful to draw a picture in ambiguous situations.

QUESTION 10:

What is the cosine of the angle between the two unit vectors represented by q_u = (0.0, 1)^T and z_u = (-0.5, -0.866)^T ?