Unit vectors along the mutually perpendicular x,y,z axes are $\hat i,\hat j,\hat k$. Two vectors a,b lie in z = 0 and satisfy $\mathbf a\ne\alpha\mathbf b$ for every scalar α. A vector perpendicular to both is
The vectors lie in the xy plane and are not parallel, so they span that plane. A vector perpendicular to both must be along its normal, the z-axis. The listed vector $\hat k$ has zero dot product with every vector of the form $(x,y,0)$, making A correct.
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