Math Help - Cross Product Help

1. Cross Product Help

Find all the vectors u that satisfy the equation <1,1,1> X u = <0,0,1>

I don't know if there are multiple ways of doing this, but we're using the determinant! :)
(The answer in the back of the book is <u3-1, u3+1, u3> I just don't know how to get to it!)

2. Re: Cross Product Help

Find all the vectors u that satisfy the equation <1,1,1> X u = <0,0,1>

I don't know if there are multiple ways of doing this, but we're using the determinant!
(The answer in the back of the book is <u3-1, u3+1, u3> I just don't know how to get to it!)
Write \displaystyle \begin{align*} \mathbf{u} = \end{align*}, then \displaystyle \begin{align*} <1, 1, 1> \times &= \left| \begin{matrix} i & j & k \\ 1 & 1 & 1 \\ x & y & z \end{matrix} \right| \end{align*}. Evaluate this determinant, and then set the resulting i component to 0, the resulting j component to 0, and the resulting k component to 1 to solve for x, y, z.

3. Re: Cross Product Help

Could you possibly show me how to solve from there? This is where I originally got stuck... lol