I want to use Mathematica to calculate the angle between two vectors (say
b) that don't lie in the same plane. The vectors are of the same length (156) have a dot product with a unit vector that's normal to a plane that their projections lie that's the same (90). Their projection vectors onto this plane are denoted by
q respectively. The angle between
q is 120 degrees.
$Assumptions = (a | e) ∈ Vectors[3, Reals] && e.e == 1 && a.e == b.e == 90 && Sqrt[a.a] == 156 == Sqrt[b.b]; p = a - (a.e) e; q = b - Dot[b, e] e; Simplify[TensorExpand[a.b], Sqrt[a.a] == 156 == Sqrt[b.b]]