Okay, a few mistakes there.
You wrote your two column vectors like this:
You SHOULD write them with a dot in between them. When you put a multiply sign in between them it means something else (in fact, a cross represents the "cross" or "vector" product of them  that's something else entirely!)
So write it with a dot, yeah?
Also, when you worked out the magnitude of the vectors, you seem to have gone wrong.
The MAGNITUDE of a vector (its "length") is just a number, not a vector.
For for the vector
a = (1,2,3)

a = SQUARE ROOT OF [ 1^2 + 2^2 + 3^2 ]
Are you happy with that? It comes straight from a 3D version of Pythagoras' Theorem.