Answer
(a) the set is orthogonal.
(b) the set is not orthonormal.
(c) the set is not a basis for $R^4$.
Work Step by Step
Let $u=(-6,3,2,1)$ and $v=(2,0,6,0)$, then we have
(a) since $u\cdot v=-12+0+12+0=0$, then the set is orthogonal.
(b) since $\|u\|=36+ 9+4+1=50\neq 1$, then the set it is not orthonormal.
(c) sine $R^4$ has dimension $4$ and the set has two vectors, then it is not a basis for $R^4$.
