Let and . For what value(s) of h is b in the plane spanned by and ?
You are asking for what does there exists real numbers so that ?
This leads to the equations,
We want this system to be consistent i.e. it has solutions.
Convert this equation into a matrix,
Now use Gauss-Jordan elimination to reduce it you should get on the bottom row something like: .
Then in order for it to be consider that expression of needs to be equal to zero.