anonymous
  • anonymous
Find a parametric representation for the surface. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of u and/or v.) The plane through the origin that contains the vectors i − j and j − k.
OCW Scholar - Multivariable Calculus
chestercat
  • chestercat
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baru
  • baru
the given vectors are A=<1, -1, 0> and B=<0, 1, -1> a vector normal to both A and B is given by cross product N= A X B N=<1, -1, 0> X <0, 1, -1> = <1, 1, 1> we know that equation of a plane is in the form ax+by+cz=d and N= substitute the components of N, we get the plane x + y +z =d we know that (0,0,0) is a point on the plane, substitute for x,y and z in the above equation to get d=0 thus x+y+z=0 is the required plane. let x=u and y=v then z=-u-v thus equation of the surface in parametric form s: (u, v, -u-v)

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