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qu  =  (0.0, 1)T and ru  =  (0.5, 0.866)T ?


qu  · ru   =   cos θ   =  0.866.    So θ   =  arc cos 0.866  =  30°.

More Practice

More Practice

The picture shows qu and ru and the angle between them.

Recall that qu · ru = ru · qu . The angle between the two vectors must be 180° or less (by definition). It does not matter which vector is first in the dot product.

Sometimes (especially when vectors point into different quadrants) it helps to draw a picture to check that your answer makes sense.


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