Question

determine o versor do vetor v=(-5,2,3)

Answer 1

(-3√14/14)² + (√14/14)² + (√14/7)² 
9*14/196 + 14/196 + 14/49 
126/196 + 14/196 + 14/49 
140/196 + 14/49 
(6860 + 2744) / 9604 
9604 / 9604 = 1

Answer 2

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

  $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf \hat{v}= \bigg(\frac{-5}{\sqrt{38}},\,\frac{2}{\sqrt{38}},\,\frac{3}{\sqrt{38}}\bigg)\:\:\:}}\end{gathered} }$

Seja o vetor "v":

           $\Large\displaystyle\begin{gathered} \vec{v} = (-5, 2, 3)\end{gathered}$

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

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

                $\Large\displaystyle\text{ \begin{gathered} = \frac{(-5, 2, 3)}{\sqrt{(-5)^{2} + 2^{2} + 3^{2}}}\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \frac{(-5, 2, 3)}{\sqrt{25 + 4+ 9}}\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \frac{(-5, 2, 3)}{\sqrt{38}}\end{gathered} }$

                $\Large\displaystyle\text{ \begin{gathered} = \bigg(\frac{-5}{\sqrt{38}},\,\frac{2}{\sqrt{38}},\,\frac{3}{\sqrt{38}}\bigg)\end{gathered} }$

✅ Portanto, o vetor versor de "v" é:

            $\Large\displaystyle\text{ \begin{gathered} \hat{v}= \bigg(\frac{-5}{\sqrt{38}},\,\frac{2}{\sqrt{38}},\,\frac{3}{\sqrt{38}}\bigg)\end{gathered} }$

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

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