Q: Describe the locus of points that satisfy the equation:

$\displaystyle

r \wedge a = b

$

where $\displaystyle

\begin{array}{l}

a = (1,1,0) \\

b = (1, - 1,0) \\

\end{array}

$.

My thinking was that the locus is either a line or a plane, where b is perpendicular to a, but I'm not entirely sure which one it is. Help would be loved.