Bonsoir,
-----------------------------------------------------------------------------------------------------
Rappel de cours :
Soient a,b,c trois vecteurs du plan. Soit λ un réel strictement positif.
i) (a, b)+(b, c) = (a, c)
ii) (a, b) = -(b, a)
-----------------------------------------------------------------------------------------------------
Soient les angles orientés (u, v) = π/6 [2π] et (w, v) = π/4 [2π] dans le plan.
1) (u, w) = (u, v)+(v, w) = (u, v)-(w, v) = (π/6)-(π/4) = (2π/12)-(3π/12) = -π/12 [2π]
2) (v, 2u) = (v, u)+(u, 2u) = -(u, v)+(u, 2u) = -(π/6)+0 = -π/6 [2π]
3) (-u, v) = (-u, u)+(u, v) = -π+(π/6) = (-6π/6)+(π/6) = -5π/6 [2π]
4) (v, w) = -(w, v) = -π/4 [2π]
5) (u, 2v) = (u, v)+(v, 2v) = (π/6)+0 = π/6 [2π]
6) (-4u, 3v) = (-4u, u)+(u, v)+(v, 3v) = -π+(π/6)+0 = -5π/6 [2π]
