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Re: Re: vectors

  • Subject: [mg3219] Re: [mg3174] Re: vectors
  • From: penny at (Des Penny)
  • Date: 17 Feb 1996 21:21:19 -0600
  • Approved:
  • Distribution: local
  • Newsgroups: wri.mathgroup
  • Organization: Wolfram Research, Inc.
  • Sender: daemon at

>Can anyone give me some direction regarding the graphing of lines
>and planes in 3D using vector equations? I'd like to convert the
>vector equation of a plane in scalar product form, ie r.n = p, to
>its graphic representation, for example.
>Paul Marshall

Hi Paul:

Lets say you want to find and plot the plane passing through the point
whose position vector is r0.  The plane must be perpendicular to n.


The position vector r is a position vector of any point in the plane.
Since the vector r-r0 must lie in the plane and therefore be perpendicular
to n, we have the equation of the plane as:

eq=  (r-r0).n==0

This returns the equation of the plane and stores this equation in "eq".
We now solve this equation for z in terms of x and y and plot the plane as

sol=  Solve[eq,z];
Plot3D[z /. sol[[1]], {x,3,5},{y,0,2}];

Hope this helps,


Des Penny

Des Penny
Physical Science Dept.
Southern Utah University
Cedar City, UT 84720

VOICE: (Office): (801) 586-7708
       (Home)  : (801) 586-2286
FAX:    (801) 865-8051
e-mail: penny at

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