Question

calcular as coordenadas do vetor w tal que w=(5,0,-4)-1/2(1,2,1)+3/5(1,-1,1)

( 51/10, -8/5, -39/10 )
( 1/3, -8/5, 3/10 )
( 10, 5, 10 )
( 51, -8, -39 )
( -51, -39, 8 )

Answer 1

Olá

1ª alternativa é a correta.

Basta desenvolver a conta, multiplicando o escalar pelo vetor, e depois somar as coordenadas x com x , y com y, e z com z.

$\displaystyle \vec{w}=(5,0,-4)- \frac{1}{2} (1,2,1)+ \frac{3}{5}(1,-1,1) \\ \\ \\ \vec{w}=(5,0,-4)-( \frac{1}{2} , \frac{2}{2} , \frac{1}{2} )+ (\frac{3 }{5} ,- \frac{3}{5, }, \frac{3}{5} ) \\ \\ \\ \vec{w}=(5- \frac{1}{2}+ \frac{3}{5} ~~,~~0-1- \frac{3}{5} ~~,~~-4- \frac{1}{2} + \frac{3}{5} ) \\ \\ \\ \vec{w}=( \frac{50-5+6}{10}~~,~~ \frac{0-5-3}{5}~~,~~ \frac{-40-5+6}{10} ) \\ \\ \\ \boxed{\vec{w}= (\frac{51}{10} , -\frac{8}{5} ,- \frac{39}{10} )}$



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