Question

dados os vetores u=(3,0,1) e v=(-2,1,2),determinar proj-u e proj-v

Answer 1

Bom dia Adrian

u = (3, 0, 1) , v = (-2, 1, 2)

comp u(v) = u.v/lul = (-6 + 0 + 2)/(√(3² + 0² + 1²) = -4/√10

proj u(v) = u.v/lul² * u
proj u(v) = -4/10* (3,0,1) = -2/5 *(3,0,1) = (-6/5, 0, -2/5)

comp v(u) = v.u/lvl = (-6 + 0 + 2)/(√(2² + 1² + 2²) = -4/3

proj v(u) = v.u/lvl² * v
proj v(u) = -4/9 * (-2, 1, 2) = (8/9, -4/9, -8/9)