Question

considere o vetor u=(4,2), determine o valor do seu versor.

Answer 1

$v= \frac{u}{|u|} \\ \\ |u|= \sqrt{ 4^{2} +2^{2} } \\ \\ |u|= \sqrt{20} \\ \\ v= [ \frac{4}{\sqrt{20}} ; \frac{2}{\sqrt{20}} ]$

Answer 2

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

  $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf \hat{u}= \bigg(\frac{2\sqrt{5}}{5},\,\frac{\sqrt{5}}{5}\bigg)\:\:\:}}\end{gathered} }$

Seja o vetor "v":

          $\Large\displaystyle\begin{gathered} \vec{u} = (4, 2)\end{gathered}$

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

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

                $\Large\displaystyle\text{ \begin{gathered} = \frac{(4, 2)}{\sqrt{4^{2} + 2^{2}}}\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \frac{(4, 2)}{\sqrt{16 + 4}}\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \frac{(4, 2)}{\sqrt{20}}\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \bigg(\frac{4}{\sqrt{20}},\,\frac{2}{\sqrt{20}}\bigg)\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \bigg(\frac{2\sqrt{5}}{5},\,\frac{\sqrt{5}}{5}\bigg)\end{gathered} }$

✅ Portanto, o vetor versor de "v" é:

            $\Large\displaystyle\text{ \begin{gathered} \hat{u}= \bigg(\frac{2\sqrt{5}}{5},\,\frac{\sqrt{5}}{5}\bigg)\end{gathered} }$

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

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