Consider the points in
. Determine the cosines of the angles of the triangle whose vertices are on these points.
Let denote the angle between
and
, let
denote the angle between
and
and let
denote the angle between
and
. Then we compute the cosines,
The answer is incorrect here. As Refael says, one needs to take differences between vectors. Then you also need to align vectors in such a way that every pair of vectors originates from the same point: BC vs BA, AB vs AC, and CA vs CB: the sum of the angles has to be pi in a triangle.
That reasoning is wrong. Let A, B and C the given vectors. So, what we want is the angle between the vectors B-C and A-C, B-A and C-A, C-B and A-B.