Dados os vetores u=(3,-1) e v=(-1,2), determinar o vetor w tal que:
a) 4(u-v)+1/3w=2u-w
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Boa noite Carolina!
Solução!
![4(\overrightarrow{U}- \overrightarrow{V})+ \dfrac{ \overrightarrow{1W}}{3}= 2\overrightarrow{U}- \overrightarrow{W}\\\\\\
\dfrac{ \overrightarrow{1W}}{3}+\overrightarrow{W}= -4(\overrightarrow{U}- \overrightarrow{V})+2\overrightarrow{U}\\\\\\\
\dfrac{ \overrightarrow{1W}}{3}+\overrightarrow{W}= (\overrightarrow{-4U}+\overrightarrow{4V})+2\overrightarrow{U}\\\\\\\
\dfrac{ \overrightarrow{1W}}{3}+\overrightarrow{W}= \overrightarrow{(-2U}+\overrightarrow{4V})\\\\\\\](https://tex.z-dn.net/?f=+4%28%5Coverrightarrow%7BU%7D-+%5Coverrightarrow%7BV%7D%29%2B++%5Cdfrac%7B+%5Coverrightarrow%7B1W%7D%7D%7B3%7D%3D++2%5Coverrightarrow%7BU%7D-+%5Coverrightarrow%7BW%7D%5C%5C%5C%5C%5C%5C%0A%0A+%5Cdfrac%7B+%5Coverrightarrow%7B1W%7D%7D%7B3%7D%2B%5Coverrightarrow%7BW%7D%3D+-4%28%5Coverrightarrow%7BU%7D-+%5Coverrightarrow%7BV%7D%29%2B2%5Coverrightarrow%7BU%7D%5C%5C%5C%5C%5C%5C%5C%0A%0A+%5Cdfrac%7B+%5Coverrightarrow%7B1W%7D%7D%7B3%7D%2B%5Coverrightarrow%7BW%7D%3D+%28%5Coverrightarrow%7B-4U%7D%2B%5Coverrightarrow%7B4V%7D%29%2B2%5Coverrightarrow%7BU%7D%5C%5C%5C%5C%5C%5C%5C%0A%0A+%5Cdfrac%7B+%5Coverrightarrow%7B1W%7D%7D%7B3%7D%2B%5Coverrightarrow%7BW%7D%3D+%5Coverrightarrow%7B%28-2U%7D%2B%5Coverrightarrow%7B4V%7D%29%5C%5C%5C%5C%5C%5C%5C%0A%0A+%0A "4(\overrightarrow{U}- \overrightarrow{V})+ \dfrac{ \overrightarrow{1W}}{3}= 2\overrightarrow{U}- \overrightarrow{W}\\\\\\
\dfrac{ \overrightarrow{1W}}{3}+\overrightarrow{W}= -4(\overrightarrow{U}- \overrightarrow{V})+2\overrightarrow{U}\\\\\\\
\dfrac{ \overrightarrow{1W}}{3}+\overrightarrow{W}= (\overrightarrow{-4U}+\overrightarrow{4V})+2\overrightarrow{U}\\\\\\\
\dfrac{ \overrightarrow{1W}}{3}+\overrightarrow{W}= \overrightarrow{(-2U}+\overrightarrow{4V})\\\\\\\")
![\dfrac{ \overrightarrow{1W}}{3}+\overrightarrow{W}= (\overrightarrow{-2(3,-1)}+(\overrightarrow{4(-1,2})\\\\\\\
\dfrac{ \overrightarrow{1W}}{3}+\overrightarrow{W}= \overrightarrow{(-10,10)}\\\\\\\
\overrightarrow{1W}+\overrightarrow{3W}= \overrightarrow{3(-10,10)}\\\\\\\
\overrightarrow{4W}= \overrightarrow{3(-10,10)}\\\\\\\
\overrightarrow{4W}= \overrightarrow{(-30,30)}\\\\\\\
\overrightarrow{W}= \dfrac{-30}{4}, \dfrac{30}{4} \\\\\\\
\overrightarrow{W}= \dfrac{-15}{2}, \dfrac{15}{2}](https://tex.z-dn.net/?f=+%5Cdfrac%7B+%5Coverrightarrow%7B1W%7D%7D%7B3%7D%2B%5Coverrightarrow%7BW%7D%3D+%28%5Coverrightarrow%7B-2%283%2C-1%29%7D%2B%28%5Coverrightarrow%7B4%28-1%2C2%7D%29%5C%5C%5C%5C%5C%5C%5C%0A%0A+%5Cdfrac%7B+%5Coverrightarrow%7B1W%7D%7D%7B3%7D%2B%5Coverrightarrow%7BW%7D%3D+%5Coverrightarrow%7B%28-10%2C10%29%7D%5C%5C%5C%5C%5C%5C%5C%0A%0A+%5Coverrightarrow%7B1W%7D%2B%5Coverrightarrow%7B3W%7D%3D+%5Coverrightarrow%7B3%28-10%2C10%29%7D%5C%5C%5C%5C%5C%5C%5C%0A%0A%0A%5Coverrightarrow%7B4W%7D%3D+%5Coverrightarrow%7B3%28-10%2C10%29%7D%5C%5C%5C%5C%5C%5C%5C%0A%0A%5Coverrightarrow%7B4W%7D%3D+%5Coverrightarrow%7B%28-30%2C30%29%7D%5C%5C%5C%5C%5C%5C%5C%0A%0A%5Coverrightarrow%7BW%7D%3D+%5Cdfrac%7B-30%7D%7B4%7D%2C+%5Cdfrac%7B30%7D%7B4%7D+%5C%5C%5C%5C%5C%5C%5C%0A%0A+%5Coverrightarrow%7BW%7D%3D+%5Cdfrac%7B-15%7D%7B2%7D%2C+%5Cdfrac%7B15%7D%7B2%7D "\dfrac{ \overrightarrow{1W}}{3}+\overrightarrow{W}= (\overrightarrow{-2(3,-1)}+(\overrightarrow{4(-1,2})\\\\\\\
\dfrac{ \overrightarrow{1W}}{3}+\overrightarrow{W}= \overrightarrow{(-10,10)}\\\\\\\
\overrightarrow{1W}+\overrightarrow{3W}= \overrightarrow{3(-10,10)}\\\\\\\
\overrightarrow{4W}= \overrightarrow{3(-10,10)}\\\\\\\
\overrightarrow{4W}= \overrightarrow{(-30,30)}\\\\\\\
\overrightarrow{W}= \dfrac{-30}{4}, \dfrac{30}{4} \\\\\\\
\overrightarrow{W}= \dfrac{-15}{2}, \dfrac{15}{2}")
Boa noite!
Bons estudos1
Solução!
Boa noite!
Bons estudos1
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