Find Orthonormal Basis of R3: u1,u2,u3

[morsel]

Homework Statement

Note: the vectors are column vectors, not row vectors. Latex is not working for me right now.

Find an orthonormal basis u1, u2, u3 of R3 such that
span(u1) =
span [1 2 3]

and

span(u1,u2) =
span { [1 2 3], [1 1 -1] }

Homework Equations

The Attempt at a Solution

Let v1=[1 2 3] and v2=[1 1 -1]
Then u1=1/(sqrt14)[1 2 3] and u2=1/(sqrt3)[1 1 -1]

But how do I get u3 without v3?

Thanks in advance!

 

[Dick]

Find a vector that's orthogonal to both u1 and u2. A cross product would come in handy.