Answer
(a) the set is orthogonal.
(b) the set is not orthonormal.
(c) the set is not a basis for $R^3$.
Work Step by Step
Let $u=(2,5,-3)$ and $v=(4,2,6)$, then we have
(a) since $u\cdot v=8+10-18=-0$, then the set is orthogonal.
(b) since $\|u\|=4+25+9=38\neq 1$, then the set it is not orthonormal.
(c) sine $R^3$ has dimension $3$ and the set has two vectors, then it is not a basis for $R^3$.
