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Q. about Solve as applied to vector equations


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 on Solaris 2.5,
running on a Sun ultra-1.

Any help will be greatly appreciated.


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