Question

Dados los vectores u→=(0,2,−3); v→=(3,0,1) . Calcular: M=(u→+3v→)⋅(3u→−5v→)

Answer 1

Al realizar las operaciones de vectores se obtiene:

M = (-135; -18; 0)

Explicación paso a paso:

Datos;

• u = (0, 2, -3)
• v = (3, 0, 1)

Calcular: M=(u+3v)⋅(3u−5v)

Aplicar producto de un escalar por un vector;

3v = 3(3, 0, 1)

3v = (9, 0, 3)

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

3u = (0, 6, -9)

5v = 5(3, 0, 1)

5v = (15, 0, 5)

Sustituir;

u + 3v = (0, 2, -3)+(9, 0, 3)

u + 3v = (0+9; -3+0; -3+3)

u + 3v = (9, -3, 0)

3u - 5v = (0, 6, -9)-(15, 0, 5)

3u - 5v = (0-15; 6-0; -9-5)

3u - 5v = (-15, 6, -14)

Aplicar producto de vectores;

M = (9, -3, 0)⋅(-15, 6, -14)

M = (9*-15; -3*6; 0*-14)

M = (-135; -18; 0)