How do I determine which space these vectors span?

Hi guys. I'm gonna right down two different problems. The first one I understand but not the second. Find the space the vectors span.

1. a=(3,5,0) b=(1,2,0) sp(a,b)= $\displaystyle (3\alpha+\beta, 5\alpha+2\beta, 0) \rightarrow sp(a,b) = (\lambda_1, \lambda_2, 0)$

2. c=(1,1,2) d=(1,0,1) sp(c,d) = $\displaystyle (\alpha+\beta, \alpha, 2\alpha+\beta) \rightarrow sp(c,d) = ???$

How do I continue to get an answer like the first question - something of the form $\displaystyle (\lambda_1, 0, \lambda_2)$...(I know that's not correct, just giving an example)