Question

Verifique ,através de um exemplo que o vetor resultante $\frac{1}{|v|} *v$ é unitário, qualquer que seja o vetor v≠0.

Answer 1

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.

$Primeiro~~ exemplo!\\\\\ \dfrac{1}{|v|} \times v\\\\\\\ \vec{v}=(3,4)\\\\\\\ |\vec{v}|= \sqrt{3^{2}+4^{2}}\\\\\\\ |\vec{v}|= \sqrt{9+16}\\\\\\\ |\vec{v}|= \sqrt{25}\\\\\\\ |\vec{v}|=5\Rightarrow ~~O ~~vetorv~~ n\~ao~~ e~~ unitario,veja~~ que ~~o\\\\\ ~~ modulo~~ e~~ diferente ~~de ~~1$



$Segundo~~exemplo!\\\\\\\\ \vec{u}=\left ( \dfrac{1}{ \sqrt{2} }, \dfrac{1}{ \sqrt{2} }\right )\\\\\\\\\\\ |\vec{u}|= \sqrt{\left ( \dfrac{1}{ \sqrt{2} }\right )+\left ( \dfrac{1}{ \sqrt{2} }\right ) }\\\\\\\ |\vec{u}|= \sqrt{\left ( \dfrac{1}{ \sqrt{2} }\right )^{2} +\left ( \dfrac{1}{ \sqrt{2} }\right )^{2} }$

$|\vec{u}|= \sqrt{\left ( \dfrac{1}{ 2 }\right ) +\left ( \dfrac{1}{ 2 }\right ) }$

$|\vec{u}|=\sqrt{\left ( \dfrac{2}{ 2 } \right )$


$|\vec{u}|=\sqrt{\left ( 1 } \right )$


$|\vec{u}|=1\Rightarrow ~~Veja~~modulo~~do~~vetor~~igual~~a~~1\\\\\\ logo~~ele~~e~~unitario,$

Boa tarde! 
Bons estudos!