Find a basis for the subspace of vectors orthogonal to <1,2,1>.
Let the vectors orthogonal to <1, 2, 1> be <a, b, c>. Equating the dot product to zero gives a + 2b + c = 0 => a = -2b - c.
Then vectors orthogonal to <1, 2, 1> have the form <-2b - c, b, c>.
One possible basis is therefore the pair of vectors <-2, 1, 0> and <-1, 0, 1> since they are clearly independent and span.
Spanning: <-2b - c, b, c> = b<-2, 1, 0> + c <-1, 0, 1>