I have two simple vector equations:

and:

: ( being the vector (aka cross) product).

I know , and all values of . I want to findsensiblevalues 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.