Verifique ,através de um exemplo que o vetor resultante 
é unitário, qualquer que seja o vetor v≠0.
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Boa tarde!
Solução!
Para que o vetor seja unitário,o modulo do vetor tem que ser igual a 1,ou seja é só calcular o modulo.
![Primeiro~~ exemplo!\\\\\
\dfrac{1}{|v|} \times v\\\\\\\
\vec{v}=(3,4)\\\\\\\
|\vec{v}|= \sqrt{3^{2}+4^{2}}\\\\\\\
|\vec{v}|= \sqrt{9+16}\\\\\\\
|\vec{v}|= \sqrt{25}\\\\\\\
|\vec{v}|=5\Rightarrow ~~O ~~vetorv~~ n\~ao~~ e~~ unitario,veja~~ que ~~o\\\\\ ~~ modulo~~ e~~ diferente ~~de ~~1\\\\\\\](https://tex.z-dn.net/?f=+Primeiro%7E%7E+exemplo%21%5C%5C%5C%5C%5C%0A%5Cdfrac%7B1%7D%7B%7Cv%7C%7D+%5Ctimes+v%5C%5C%5C%5C%5C%5C%5C%0A%5Cvec%7Bv%7D%3D%283%2C4%29%5C%5C%5C%5C%5C%5C%5C%0A%7C%5Cvec%7Bv%7D%7C%3D+%5Csqrt%7B3%5E%7B2%7D%2B4%5E%7B2%7D%7D%5C%5C%5C%5C%5C%5C%5C%0A%7C%5Cvec%7Bv%7D%7C%3D+%5Csqrt%7B9%2B16%7D%5C%5C%5C%5C%5C%5C%5C%0A%7C%5Cvec%7Bv%7D%7C%3D+%5Csqrt%7B25%7D%5C%5C%5C%5C%5C%5C%5C%0A%7C%5Cvec%7Bv%7D%7C%3D5%5CRightarrow+%7E%7EO+%7E%7Evetorv%7E%7E+n%5C%7Eao%7E%7E+e%7E%7E+unitario%2Cveja%7E%7E+que+%7E%7Eo%5C%5C%5C%5C%5C+%7E%7E+modulo%7E%7E+e%7E%7E+diferente+%7E%7Ede+%7E%7E1%5C%5C%5C%5C%5C%5C%5C+++++++ "Primeiro~~ exemplo!\\\\\
\dfrac{1}{|v|} \times v\\\\\\\
\vec{v}=(3,4)\\\\\\\
|\vec{v}|= \sqrt{3^{2}+4^{2}}\\\\\\\
|\vec{v}|= \sqrt{9+16}\\\\\\\
|\vec{v}|= \sqrt{25}\\\\\\\
|\vec{v}|=5\Rightarrow ~~O ~~vetorv~~ n\~ao~~ e~~ unitario,veja~~ que ~~o\\\\\ ~~ modulo~~ e~~ diferente ~~de ~~1\\\\\\\")
![Segundo~~exemplo!\\\\\\\\
\vec{u}=\left ( \dfrac{1}{ \sqrt{2} }, \dfrac{1}{ \sqrt{2} }\right )\\\\\\\\\\\
|\vec{u}|= \sqrt{\left ( \dfrac{1}{ \sqrt{2} }\right )+\left ( \dfrac{1}{ \sqrt{2} }\right ) }\\\\\\\
|\vec{u}|= \sqrt{\left ( \dfrac{1}{ \sqrt{2} }\right )^{2} +\left ( \dfrac{1}{ \sqrt{2} }\right )^{2} }\\\\\\\](https://tex.z-dn.net/?f=Segundo%7E%7Eexemplo%21%5C%5C%5C%5C%5C%5C%5C%5C%0A+%5Cvec%7Bu%7D%3D%5Cleft+%28+%5Cdfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D%2C+%5Cdfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D%5Cright+%29%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%7C%5Cvec%7Bu%7D%7C%3D+%5Csqrt%7B%5Cleft+%28+%5Cdfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D%5Cright+%29%2B%5Cleft+%28+%5Cdfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D%5Cright+%29+%7D%5C%5C%5C%5C%5C%5C%5C%0A%7C%5Cvec%7Bu%7D%7C%3D+%5Csqrt%7B%5Cleft+%28+%5Cdfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D%5Cright+%29%5E%7B2%7D++%2B%5Cleft+%28+%5Cdfrac%7B1%7D%7B+%5Csqrt%7B2%7D+%7D%5Cright+%29%5E%7B2%7D++%7D%5C%5C%5C%5C%5C%5C%5C+%0A%0A%0A%0A%0A%0A+ "Segundo~~exemplo!\\\\\\\\
\vec{u}=\left ( \dfrac{1}{ \sqrt{2} }, \dfrac{1}{ \sqrt{2} }\right )\\\\\\\\\\\
|\vec{u}|= \sqrt{\left ( \dfrac{1}{ \sqrt{2} }\right )+\left ( \dfrac{1}{ \sqrt{2} }\right ) }\\\\\\\
|\vec{u}|= \sqrt{\left ( \dfrac{1}{ \sqrt{2} }\right )^{2} +\left ( \dfrac{1}{ \sqrt{2} }\right )^{2} }\\\\\\\")
![|\vec{u}|= \sqrt{\left ( \dfrac{1}{ 2 }\right ) +\left ( \dfrac{1}{ 2 }\right ) }\\\\\\\](https://tex.z-dn.net/?f=%7C%5Cvec%7Bu%7D%7C%3D+%5Csqrt%7B%5Cleft+%28+%5Cdfrac%7B1%7D%7B+2+%7D%5Cright+%29++%2B%5Cleft+%28+%5Cdfrac%7B1%7D%7B+2+%7D%5Cright+%29++%7D%5C%5C%5C%5C%5C%5C%5C%0A%0A "|\vec{u}|= \sqrt{\left ( \dfrac{1}{ 2 }\right ) +\left ( \dfrac{1}{ 2 }\right ) }\\\\\\\")
Boa tarde!
Bons estudos!
Solução!
Para que o vetor seja unitário,o modulo do vetor tem que ser igual a 1,ou seja é só calcular o modulo.
Boa tarde!
Bons estudos!
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