I am supposed to use a secondary justification (other than using the inverse cosine of the dot product divided by magnitude) that the angle between two vectors (117.429 degrees) is obtuse. The two vectors are:
A: <5,0,2>
B: <-6,2,5>
My secondary explanation was that the projection of A onto B contains more than half of the magnitude of B (e.g. the magnitude of the projection of A onto B is less than 50 % different from the magnitude of B), so the angle between the vectors is greater than 90 degrees.
$|\frac{Norm[Projection[X,Y]] - Norm[Y]}{Norm[Y]}|$ = 69.2%>50%
Does this make sense why the angle would be obtuse, and are there any counterexamples to this?