Question

Como achar o vetor unitário na direção do vetor V= (-3/2,2,-1)?

Answer 1

O versor unitário do vetor "v" (-3/2,2,-1) é dado por:

$u=\frac{V}{||V||} \\ \\ u=\frac{(-\frac{3}{2},2,-1)}{\sqrt{(-\frac{3}{2})^2+2^2+(-1)^2}} \\ \\ u=\frac{(-\frac{3}{2},2,-1)}{\sqrt{\frac{9}{4}+4+1}} \\ \\ u=\frac{(-\frac{3}{2},2,-1)}{\sqrt{\frac{9}{4}+5}} \\ \\ u=\frac{(-\frac{3}{2},2,-1)}{\sqrt{\frac{9+20}{4}}} \\ \\ u=\frac{(-\frac{3}{2},2,-1)}{\sqrt{\frac{29}{4}}} \\ \\ u=\frac{-\frac{3}{2}}{\sqrt{\frac{29}{4}}},\frac{2}{\sqrt{\frac{29}{4}}},\frac{-1}{\sqrt{\frac{29}{4}}}$

Simplificando:

$u=\frac{-\frac{3}{2}}{\sqrt{\frac{29}{4}}},\frac{2}{\sqrt{\frac{29}{4}}},\frac{-1}{\sqrt{\frac{29}{4}}} \\ \\ u=\frac{-\frac{3}{2}}{\sqrt{\frac{29}{4}}} \\ \\ u=(-\frac{3}{2}).(\frac{1}{\sqrt{\frac{29}{4}}}) \\ \\ u=\left(\begin{array}{ccc}-\frac{3}{2\sqrt{\frac{29}{4}}},\frac{2}{\sqrt{\frac{29}{4}}},\frac{-1}{\sqrt{\frac{29}{4}}}\end{array}\right)$

Se fizer o módulo desse vetor, o resultado será 1.