Question

encontre o versor do vetor (8,-15)

Answer 1

Olá


Podemos encontrar o versor de um vetor a partir da seguinte 'fórmula'

$\displaystyle \frac{\vec{u}}{|\vec{u}|}$

Ou seja, basta dividir o vetor pelo o módulo do mesmo.


u = (8, -15)

Encontrando o módulo

$|\vec{u}|\mathsf{= \sqrt{8^2+(-15)^2} }\\\\\mathsf{= \sqrt{64+225} }\\\\\mathsf{= \sqrt{289} }\\\\|\vec{u}|=17$


O versor de u fica sendo

$\displaystyle \boxed{\mathsf{\left( \frac{8}{17},- \frac{15}{17} \right)}}$

Answer 2

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

  $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf \hat{v} = \bigg(\frac{8}{17},\,-\frac{15}{17}\bigg)\:\:\:}}\end{gathered} }$

Seja o vetor "v":

          $\Large\displaystyle\begin{gathered} \vec{v} = (8, -15)\end{gathered}$

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

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

                $\Large\displaystyle\text{ \begin{gathered} = \frac{(8, -15)}{\sqrt{8^{2} + (-15)^{2}}}\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \frac{(8, -15)}{\sqrt{64 + 225}}\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \frac{(8, -15)}{\sqrt{289}}\end{gathered} }$

                $\Large\displaystyle\begin{gathered} = \bigg(\frac{8}{17},\,-\frac{15}{17}\bigg)\end{gathered}$

✅ Portanto, o vetor versor de "v" é:

            $\Large\displaystyle\begin{gathered} \hat{v}= \bigg(\frac{8}{17},\,-\frac{15}{17}\bigg)\end{gathered}$

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

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