Find the cross product axb and verify it is orthogonal to both a and b

a = <e^2t, 1, e^-t>

b = <e^t, 2, e^-t>

I calculated the cross product to be <-e^-t, e^t - 1, 2e^2t - e^t> and tried dotting it with a and b. Problem is, I don't get 0 in either case. Isn't that how you show it is orthogonal?