Suggestions for hint and solution

Hi Li,

Sorry, I assumed that these vectors were in two dimensions. So my suggestions about parallel lines won't work :-(

However, it still seems that the solution can be simplified like so. Determining if any point in in both lines is equivalent to finding solutions the the following system of linear equations

${\begin{pmatrix}-1&2&|&-1\\2&-1&|&-2\\2&-1&|&2\end{pmatrix}}$

This is obtained from

$[0,2,1]+s[-1,2,2]=[-1,0,3]+t[-2,1,1]$

Best, Brian

I think the current solution is okay. But as you suggested, we can add another way to prove there's no solution to

$[0,2,1]+s[-1,2,2]=[-1,0,3]+t[-2,1,1]$

using the matrix you mentioned above.