Question

Encontra o versor do vetor u =(8-15)

Answer 1

||u||=√{ (8)^2+(-15)^2
||u||=√289
||u|=17
versor=(8,-15)/17
vs=(8/17,-15/17)

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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