Let $q$ denote a quadratic form on a real vector space $V$. Define the rank and signature of $q$.

Find the rank and signature of the following quadratic forms. (a) $q(x, y, z)=x^{2}+y^{2}+z^{2}-2 x z-2 y z$. (b) $q(x, y, z)=x y-x z$.

(c) $q(x, y, z)=x y-2 z^{2}$.