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## Homework Statement

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**

## Homework Equations

## 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?