Consider in $\mathbb{E}^3$ a cube of unit size $ABCDEFGH$.
Assume that $\mathbb{V}^3$ is oriented, and let the basis K = {AB, AC, AE} be positive. Now, consider the vector $\mathbf{v}_1 = (-1, 1,2)\mathbf{K}$ and $\mathbf{v}_2 = (-1,2,1)\mathbf{K}$.Calculate the coordinates,relative to K, of the cross product $\mathbf{v}_1$ x $\mathbf{v}_2$.
I've managed to do the cross product,which results in $(-3,-1,-1)$,wouldn't that also be relative to K?What exactly I am missing?Any help would be kindly appreciated.