Concept:
The perpendicular nature of the vector cross product.

Formula:
$$\vec{c} = \vec{a} \times \vec{b} \implies \vec{c} \perp \vec{a} \text{ and } \vec{c} \perp \vec{b}$$

Solution:
The vector cross product produces a vector that is always perpendicular to the plane containing the original vectors. If the resulting vector points along the z-axis, then both \(\vec{a}\) and \(\vec{b}\) must be perpendicular to the z-axis. This means they must lie within the flat plane perpendicular to the z-axis, which is the xy-plane.

Why other options are incorrect:

• yz-plane contains vectors whose cross products must point along the x-axis.
• zx-plane contains vectors whose cross products must point along the y-axis.