Given a = <1,2,3> and b = <1,-1,-1>, sketch the collection of all position vectors c satisfying a x b = a x c
The Attempt at a Solution
I've calculated a x b = <1,4,-3> and Defining c = <x,y,z> I found a x c = <2z-3y, z-3x, y-2x>. I want to come up with an algebraic representation of the vectors so I created the following system of equations
1 = 2z - 3y
4 = 3x - z
-3 = y - 2x
So x,y, and z that satisfy all three equations are a possible vector. I'm having trouble solving it, and I'm thinking I'm just going to get a single solution to this system If I do manage to solve it and it has a solution.
Can you help?