Question

Determine o versor do vetor v = 3i −j​

Answer 1

Resposta: v=(3√10/10;-√10/10)

Explicação passo-a-passo:

u=(1 / ||v|| )*v

v={1/√[3²+(-1)²]}*(3,-1)

v=√10/10*(3,-1)

v=(3√10/10;-√10/10)

ou

v=(0,94868;-0,31623)

Answer 2

✅ Após resolver os cálculos, concluímos que o versor do referido vetor dado é:

   $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf \hat{v} = \bigg(\frac{3\sqrt{10}}{10},\,-\frac{\sqrt{10}}{10}\bigg)\:\:\:}}\end{gathered} }$

Seja o vetor "v":

          $\Large\displaystyle\begin{gathered} \vec{v} = 3\,\vec{i} - \vec{j}= (3, -1)\end{gathered}$

O versor de um vetor é o vetor unitário que possui mesma direção e sentido do referido vetor.

           $\Large\displaystyle\text{ \begin{gathered} \hat{v} = \frac{\vec{v}}{\parallel\vec{v}\parallel}\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \frac{(3, -1)}{\sqrt{3^{2} + (-1)^{2} }}\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \frac{(3, -1)}{\sqrt{9 + 1}}\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \frac{(3, -1)}{\sqrt{10}}\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \bigg(\frac{3}{\sqrt{10}},\,-\frac{1}{\sqrt{10}}\bigg)\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \bigg(\frac{3\sqrt{10}}{10},\,-\frac{\sqrt{10}}{10}\bigg)\end{gathered} }$

✅ Portanto, o vetor versor de "v" é:

            $\Large\displaystyle\text{ \begin{gathered} \vec{v}= \bigg(\frac{3\sqrt{10}}{10},\,-\frac{\sqrt{10}}{10}\bigg)\end{gathered} }$

$\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered} }$

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