Operaciones con vectores 14
Dado un vector a = (7, 3, –4) y otro |b| = 25 y cosenos directores proporcionales a (2, –2, 1). Halla:
a) Componentes de b.
b) a·b
c) Ángulo que forman.
Solución:
Datos: a = (7, 3, –4); |b| = 25; (cos α)/2 = (cosb)/(–2) = (cosg)/1
a) Componentes de b = (x, y, z)
cos α = x/25; cos β = y/25; cos γ = z/25
(3/2) x = 25 → x = 50/3
b = (50/3, –50/3, 25/3)
b)
a·b = (7, 3, –4)· (50/3, –50/3, 25/3) = (350/3) – (150/3) – (100/3) = 100/3
c)