Difficult# Find Vectors that have a Given Cross Product with a Given Vector

MVCALC-XOERDE

Let ${\bf v}=\langle 1,0,1\rangle$ and assume that ${\bf v} \times {\bf w}=\langle 1,0,-1 \rangle$.

If the first component of ${\bf w}$ is $6$, what are the second and third components of ${\bf w}$?