Question

Considere no espaço vetorial R3 os vetores u = (1, 2, 1), v = (3, 1, -2) e w = (4, 1, 0). Marque a alternativa que indica a solução de 2u + v = 3w

Answer 1

Olá

$\vec{u}=(1,2,1)\\\vec{v}=(3,1,-2)\\\vec{w}=(4,1,0)\\\\\\\text{Para encontrar o vetor '2u', basta multiplicar cada elemento do vetor u}\\\text{por 2}\\\\2\vec{u}=2(1,2,1)\\\\\boxed{2\vec{u}=(2,4,2)}\\\\\text{A priori e a mesma para encontrar o vetor '3w'}\\\\3\vec{w}=3(4,1,0)\\\\\boxed{3\vec{w}=(12,3,0)}\\\\\\\\\text{O enunciado pede o resultado}\\\\2\vec{u}+\vec{v}=3\vec{w}\\\\\text{Passando o vetor '3w' para o outro lado}\\\\2\vec{u}+\vec{v}-3\vec{w}\\\\\text{Substitui os vetores que encontramos}$

$=(2,4,2)~+~(3,1,-2)~-~(12,3,0)\\\\=(2+3-12,~4+1-3,~2-2-0)\\\\=\boxed{\boxed{(-7,~2,~0)}}$