First note that the equation describes a plane in R^3. Specifically, recall that a plane may be specified by the set of all points whose displacement vectors from a proprietary point are normal to a specific vector, called the normal vector. Normality is defined by the dot product vanishing, so note that your equation may be rewritten as A normal vector to your plane is thus (1, -2, 1).

The two basis vectors must have a dot product of 0 to be orthogonal and must have a cross product that is a scalar multiple of the normal vector, since they must lie in that plane.