Dot Product and Angle

u.v = ||u||.||v||.cos(uˆv)

if u and v are long enough ...      (uˆv) = acos(u.v / (||u||.||v||)

Trigonometric circle

sin(0) = 0

sin(PI/2 rad) = 1

cos(0) = 1

sin(a) = opp/hyp

cos(a) = adj/hyp (Trigo + Thales)

if you know the cosine, you don't know the sign of the angle !

 

u.v = 0 <=> (u,v) orthogonal, perpendicular (Maths)

u.v <= epsilon <=> (u,v) orthogonal, perpendicular (Computing)

(or u = 0, or v = 0 ...)

Length of the perpendicular projection of v on u ??

Length = u.v / || u || = (u/||u||).v