Question

1) Matemática - Ajudaaaaaaaaaaa

Answer 1

Boa noite Ramendes!

Solução!

$\vec{u}=(2,a,1)\\\\\\\ \vec{v}=(3,1,-2)\\\\\\ \vec{w}=(3a-1,-2,4)$

Fazendo!

$\vec{u} \times \vec{v}= (2,a,-1) \times(3,1,-2)=(6+a+2)\Rightarrow(a+8)\\\\\ (\vec{u}+\vec{v})=(2,a,-1)+(3,1,-2)\Rightarrow (5,a+1,-3)$

$(\vec{v}+\vec{w})=(3,1,-2)+(2a-1,-2,4)\\\\ =(2a-1+3,1-2,-2+4)\Rightarrow (2a+2,-1,2)$

Então!

$(\vec{u}+\vec{v}) \times(\vec{v}+\vec{w})=\vec{u} \times \vec{v}\\\\\\\ [(5,a+1,-3) \times (2a+2,-1,2)]=(6+a+2)$

$[10a+10-a-1-6]=(6+a+2)\\\\\ [10a-a-a]=(8-10+7)\\\\\ [10a-2a]=(15-10)\\\\\ 8a=5\\\\\ a= \dfrac{5}{8} \\\\\\\\\\ \boxed{Resposta:a= \frac{5}{8}}$

Boa tarde!
Bons estudos!