contestada

Find a parametrization of the portion of the plane x + y + z = 5 that is contained inside the following. Inside the cylinder x^2 + y^2 = 16 Inside the cylinder y^2 + z^2 = 16

Respuesta :

LammettHash
  • Inside [tex]x^2+y^2=16[/tex]:

Set

[tex]\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=5-x(u,v)-y(u,v)=5-u(\cos v+\sin v)\end{cases}[/tex]

with [tex]0\le u\le4[/tex] and [tex]0\le v\le2\pi[/tex].

  • Inside [tex]y^2+z^2=16[/tex]:

Same as above, but swap [tex]z(u,v)[/tex] with [tex]x(u,v)[/tex], so that

[tex]\begin{cases}x(u,v)=5-u(\cos v+\sin v)\\y(u,v)=u\sin v\\z(u,v)=u\cos v\end{cases}[/tex]

again with [tex]0\le u\le4[/tex] and [tex]0\le v\le2\pi[/tex].

Otras preguntas