So I'm given the following bilinear form over $\mathbb{R}^3$:
$$f((x,y,z),(r,s,t))=2xr+axs+bry+cys+3zt$$
where $a,b,c$ are real parameters and I'm asked to find for what values of them $f$ is a scalar product and I've come up with:
$$a=b$$
$$2c>a^2$$
using the definitions of inner product (is that all one can came up with or I've missed some informations ?) however then I'm asked to find an orthonormal base and I really don't know how to proceed further. I know that I have to computer eigenvalues and so on but I can't really figure out how to deal with the parameters.