Linear Algebra Question

Question

Expand the set below to form a basis for  by adding vectors to the set.

{[1,-3,2], [5,4,0] }

The vector to add is ?

Answer 1

The span of the given vectors is a plane in R³

The cross product of the given vectors is perpendicular to those vectors (and to the plane)

The two given vectors together with the cross product vector is a basis for R³