If $B=((1,0,1),(2,1,2),(3,3,0))$ is a basis of $\mathbb{R}^3$, find a scalar product where $B$ is an orthogonal basis.
Given the standard scalar product of $\mathbb{R}^3$, to find an orthogonal basis I use the Gram-Schmidt process. However, I don't know what to do in this case where given the orthogonal basis I have to find his scalar product.
How can I start?