       Re: Re: vectors

• To: mathgroup at smc.vnet.net
• Subject: [mg3219] Re: [mg3174] Re: vectors
• From: penny at edu-suu-scf.sc.suu.edu (Des Penny)
• Date: Sat, 17 Feb 1996 14:18:32 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```>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.

In:
n={1,2,3}
r0={4,1,5}
r={x,y,z}

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:

In:
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
follows:

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

Hope this helps,

Cheers,

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 suu.edu
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