Question

Calcular o ângulo ̂ do triângulo de vértices = (−4, 7, 2), = (−1, 2, 3) e = (−3, 6, 0).​

Answer 1

Resposta:

(−1, 2, 3) – (−4, 7, 2) = (3, -5, 1) vetor "B" - "A" => 5,91 (modulo)

(−1, 2, 3) - (−3, 6, 0) = (2, -4, 3) vetor "B" - "C" => 5,38 (modulo)

("B" - "A") x ( "B" - "C") => (3, -5, 1) x (2, -4, 3) / 5,91 x 5,38 = 6 + 20 +3 / 31,79 = 29 / 31,79 = 0,91° = 24,49° (ângulo no vértice “B”)

(−4, 7, 2) - (−1, 2, 3) = (-3, 5, -1) vetor "A" - "B" => 5,91 (modulo)

(−4, 7, 2) - (−3, 6, 0) = (-1, 1, 2) vetor "A" - "C" => 2,44 (modulo)

(-3, 5, -1) x (-1, 1, 2) / 5,38 x 2,44 = 3 + 5 – 2 / 13,12 = 6 / 13,12 = 0,45° = 63,25° (ângulo no vertice “A”)

180°- 24,49° - 63,25° = 92,26° (ângulo no vértice “C”)  

Explicação passo a passo: