Question

Calcule o vetor oposto de AB→ , sendo A(1, 3) e B(0, −2).​

Answer 1

Resposta:

Explicação passo-a-passo:

Answer 2

✅ Após resolver os cálculos, concluímos que o vetor oposto procurado é:

         $\Large\displaystyle\text{ \begin{gathered} \vec{v_{o}} = (1, 5)\end{gathered} }$

Sejam os pontos:

            $\Large\begin{cases} A(1, 3)\\B(0, -2)\end{cases}$

Para calcular o vetor oposto de um determinado vetor "v" devemos utilizar a seguinte fórmula:

       $\Large\displaystyle\text{ \begin{gathered} \vec{v_{o}} = (-1)\cdot\vec{v}\end{gathered} }$

Então, temos:

       $\Large\displaystyle\text{ \begin{gathered} \vec{v_{o}} = (-1)\cdot\vec{v}\end{gathered} }$

             $\Large\displaystyle\begin{gathered} = (-1)\cdot\overrightarrow{AB}\end{gathered}$

             $\Large\displaystyle\begin{gathered} = (-1)\cdot(B - A)\end{gathered}$

             $\Large\displaystyle\begin{gathered} = (-1)\cdot[(0, -2) - (1, 3)]\end{gathered}$

             $\Large\displaystyle\begin{gathered} = (-1)\cdot[0 -1, -2 - 3]\end{gathered}$

              $\Large\displaystyle\begin{gathered} = (-1)\cdot[-1, -5]\end{gathered}$

              $\Large\displaystyle\begin{gathered} = (1, 5)\end{gathered}$

✅ Portanto, o vetor oposto procurado é:

        $\Large\displaystyle\text{ \begin{gathered} \vec{v_{o}} = (1, 5)\end{gathered} }$

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