*To*: mathgroup@smc.vnet.net*Subject*: [mg12043] Q. about Solve as applied to vector equations*From*: Rajarishi S Sinha <rsinha+@andrew.cmu.edu>*Date*: Fri, 24 Apr 1998 01:52:14 -0400*Organization*: Doctoral student, Civil and Environmental Engineering, Carnegie Mellon, Pittsburgh, PA

Hello, I'm trying to solve the following vector expression for the vector 'r': x*n1 X r1 + (1-x)*n2 X r2 = (1/norm2(x*n1 + (1-x)*n2))*(x+n1 + (1-x)*n2) X r 0<=x<=1 where x is a scalar between 0 and 1. r1 and r2 are position vectors of 2 points (say, P1 and P2) in 3-space n1 and n2 are normal vectors at P1 and P2 to some "curve", whose endpoints are P1 and P2. norm2() is the second norm function, which I define. 'X' is the cross product operator. 'r' is the generatrix for the curve, and is what I want to find. The expression is linear in 'r'. I tried to use the mathematica Solve function to solve this system, but it returned an empty list. So, I split up the system into its 3 (x,y,z) components and asked it to solve the system of 3 equations, but got the same result. Then I tried using the Reduce function on the system of 3 equations, and it's been running for the past 7 hours ! Am I wrong in trying to use Solve/Reduce to get a solution ? Is there some other workaround ? I am using Mathematica 3.0.1.1 on Solaris 2.5, running on a Sun ultra-1. Any help will be greatly appreciated. Raj -------------------------------------------------------------------- Off: 1212 Hamburg Hall, Institute for Complex Engineered Systems, Carnegie Mellon University, Pittsburgh, PA 15213, USA Phone: 412-268-5214 Fax: 412-268-5229 118F Porter Hall, Department of Civil Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA Phone: 412-268-2086 Fax: 412-268-7813 Res: 5780 Fifth Avenue, #1C, Pittsburgh, PA 15232, USA Phone: 412-361-1574 URL: http://www.cs.cmu.edu/~rsinha/home.html --------------------------------------------------------------------