Sabendo que a reta r passa pelo ponto A(2,-8,-1) e é paralela à reta s :
.Se P(-2,p,n)∈ r, determinar p e n.
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Boa tarde Lary!
Solução!
Sendo o ponto!
![A(2,-8,-1)\\\\\
r // s\\\\\\\](https://tex.z-dn.net/?f=A%282%2C-8%2C-1%29%5C%5C%5C%5C%5C%0Ar+%2F%2F+s%5C%5C%5C%5C%5C%5C%5C%0A "A(2,-8,-1)\\\\\
r // s\\\\\\\")
Fazendo!
![(x,y,z)=(2,-8,-1)+m(2,-7,1)\\\\\
P \in~r\\\\\\\
(-2,p,n)=(2,-8,-1)+m(2,-7,1)\\\\\
-2=2+2m\\\\\\
-2-2=2m\\\\\
-4=2m\\\\
m= \dfrac{-4}{2}\\\\\
m=-2](https://tex.z-dn.net/?f=%28x%2Cy%2Cz%29%3D%282%2C-8%2C-1%29%2Bm%282%2C-7%2C1%29%5C%5C%5C%5C%5C%0AP+%5Cin%7Er%5C%5C%5C%5C%5C%5C%5C%0A%28-2%2Cp%2Cn%29%3D%282%2C-8%2C-1%29%2Bm%282%2C-7%2C1%29%5C%5C%5C%5C%5C%0A-2%3D2%2B2m%5C%5C%5C%5C%5C%5C%0A-2-2%3D2m%5C%5C%5C%5C%5C%0A-4%3D2m%5C%5C%5C%5C%0Am%3D+%5Cdfrac%7B-4%7D%7B2%7D%5C%5C%5C%5C%5C%0Am%3D-2+ "(x,y,z)=(2,-8,-1)+m(2,-7,1)\\\\\
P \in~r\\\\\\\
(-2,p,n)=(2,-8,-1)+m(2,-7,1)\\\\\
-2=2+2m\\\\\\
-2-2=2m\\\\\
-4=2m\\\\
m= \dfrac{-4}{2}\\\\\
m=-2")
![(-2,p,n)=(2,-8,-1)+m(2,-7,1)\\\\\
(-2,p,n)=(2,-8,-1)-2(2,-7,1)\\\\\
(-2,p,n)=(2,-8,-1)+(-4,14,-2)\\\\\
p=-8+14\\\\
\boxed{p=6}\\\\\\
n=-1-2\\\\\
\boxed{n=-3}](https://tex.z-dn.net/?f=%28-2%2Cp%2Cn%29%3D%282%2C-8%2C-1%29%2Bm%282%2C-7%2C1%29%5C%5C%5C%5C%5C%0A%28-2%2Cp%2Cn%29%3D%282%2C-8%2C-1%29-2%282%2C-7%2C1%29%5C%5C%5C%5C%5C%0A%28-2%2Cp%2Cn%29%3D%282%2C-8%2C-1%29%2B%28-4%2C14%2C-2%29%5C%5C%5C%5C%5C%0Ap%3D-8%2B14%5C%5C%5C%5C%0A%5Cboxed%7Bp%3D6%7D%5C%5C%5C%5C%5C%5C%0An%3D-1-2%5C%5C%5C%5C%5C%0A%5Cboxed%7Bn%3D-3%7D "(-2,p,n)=(2,-8,-1)+m(2,-7,1)\\\\\
(-2,p,n)=(2,-8,-1)-2(2,-7,1)\\\\\
(-2,p,n)=(2,-8,-1)+(-4,14,-2)\\\\\
p=-8+14\\\\
\boxed{p=6}\\\\\\
n=-1-2\\\\\
\boxed{n=-3}")
Boa tarde!
Bons estudos!
Solução!
Sendo o ponto!
Fazendo!
Boa tarde!
Bons estudos!
laryduarte:
mt obg
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