Answer
all the vectors spanned by the vectors $\{(1,0,-\frac{1}{2}),(0,1,\frac{1}{2})\}$ are orthogonal to $u$.
Work Step by Step
Let $u=(1-1,2)$ and $v=(a,b,c)$ such that $u$ is orthogonal to $v$, that is
$$u\cdot v=0 \Longrightarrow a-b+2c=0.$$
Now, assume that, $a=s$ and $b=t$, then we get the solution,
$$a=s, \quad b=t, \quad c=-\frac{1}{2}s+\frac{1}{2}t$$
that is, $v=(s,t,-\frac{1}{2}s+\frac{1}{2}t)=s(1,0,-\frac{1}{2})+t(0,1,\frac{1}{2})$
Hence, all the vectors spanned by the vectors $\{(1,0,-\frac{1}{2}),(0,1,\frac{1}{2})\}$ are orthogonal to $u$.
