Question

3) Matemática - Ajudaaaaaaaaaaa

Answer 1

Boa noite!

Solução!

$\vec{|u|}=2\\\\ \vec{|v|}=3\\\\ \vec{v}\times \vec{u}=-1$

$a)\\\\\ (\vec{u}-3\vec{v}) \times \vec{u}\\\\\ (\ve{u^{2}}-3(\vec{v}\vec{u}) )\\\\\ (2^{2}-3.(-1))\\\\ 4+3=7 \Leftarrow Resposta$

$b)\\\\ (2\vec{v}-\vec{u})\times 2\vec{v}\\\\\ (4\vec{(v)}^{2}-2\vec{u}.\vec{v})\\\\\ (4(3)^{2}-2(-1)\\\\\\ (4.9+2)\\\\\ (36+2)=38\Leftarrow Resposta$

$c)\\\\ (\vec{u} + \vec{v} )\times ( \vec{v} -4 \vec{u})\\\\\\\ (\vec{u}.\vec{v} -4\vec{(u)}^{2}+ \vec{(v)^{2} }-4 \vec{u} .\vec{v}\\\\\\\ (-1-4(2)^{2}+(3)^{2} -4(-1))\\\\\\\ (-1-4.4+9+4)\\\\\\\ (-1-16+9+4)\\\\\\\ (-17+13)=-4\Leftarrow Resposta$



$d)\\\\\ (3\vec{u}+4\vec{v}) \times (-2\vec{u}-5\vec{v})\\\\\\ (-6\vec{(u)^{2} }-15\vec{u}.\vec{v}-8\vec{u}.\vec{v}-20\vec{(v)^{2}}\\\\\ (-6\vec{(u)^{2} }-23(\vec{u}.\vec{v})-20\vec{(v)^{2}}\\\\\\\ (-6(2)^{2} -23(-1)-20(3)^{2}\\\\\\\\ (-6(4)+23-20(9))\\\\\ (-24+23-180)\\\\ (-204+23)=-181 \Leftarrow Resposta$

Boa tarde!

Bons estudos!