Question

Dados os vetores a = (3, 2, -m) e b = (m/n, 1, -1), n não nulo, os valores de m e n para que a e b sejam L.D.,

A) m = -2 e n = -4/3
B) m = 2 e n = 4/3
C) m = -2 e n = 4/3
D) m = 2 e n = -4/3
E) m = 4/3 e n = 2

Answer 1

Boa noite!


Solução!


Para que os vetores sejam LD tem que serem diferentes de zero.


$a=(3,2-m)\\\\\ b=( \frac{m}{n},1,-1)$


Fazendo!


$\dfrac{3}{ \dfrac{m}{n} }= \dfrac{2}{1}= \dfrac{-m}{-1}\\\\\\\\ \dfrac{2}{1}= \dfrac{-m}{-1}\\\\\\\\\\\ -m=-2\\\\\ \boxed{m=2}\\\\\\\\\\\\\\\ \dfrac{3}{ \dfrac{m}{n} }= \dfrac{2}{1}\\\\\\\\ \dfrac{3}{ \dfrac{2}{n} }= \dfrac{2}{1}\\\\\\\ 3.\dfrac{n}{2}= \dfrac{2}{1}\\\\\\\\ \dfrac{3n}{2}= \dfrac{2}{1}\\\\\\\\ 3n=4\\\\\\\ \boxed{n= \dfrac{4}{3}}$



$\boxed{Resposta:Alternativa~~B}$


Boa noite!
Bons estudos!