I have two simple vector equations:
: ( being the vector (aka cross) product).
I know , and all values of . I want to find sensible values for the .
When n = 2 this is a simple simultaneous equation.
However when n > 2 there is no single point solution.
Consider n=3; one could view the two equations as defining planes, the intersection of these planes would then define a line of points that satisfy the two equations.
What I want is the solution from this range that minimises the largest value of .
My current thinking is set all except 2 of the to zero and solve the resulting simultaneous equation.
Repeat for a different pair of
This gives two points on the solution line.
Find the perpendicular to this line that passes through the origin (All )
Am I looking in the correct area? Can someone point the way forward please.