Always remember the key geometrical facts about scalar and cross products for non-zero vectors ${\bf u}$ and ${\bf v}$:

1) ${\bf u}\cdot {\bf v}=0$ if and only if ${\bf u}$ and ${\bf v}$ are perpendicular.

2) ${\bf u}\times {\bf v}=0$ if and only if ${\bf u}$ and ${\bf v}$ are parallel.

3) ${\bf u}\times {\bf v}$ is perpendicular to both ${\bf u}$ and ${\bf v}$.

This problem uses mathematical concepts covered in the later Further Pure Mathematics A Level Modules.