Answer
all the vectors spanned by the vectors $\{(1,0,0),(0,1,\frac{4}{3})\}$ are orthogonal to $u$.
Work Step by Step
Let $u=(0,-4,3)$ and $v=(a,b,c)$ such that $u$ is orthogonal to $v$, that is
$$u\cdot v=0 \Longrightarrow -4b+3c=0.$$
Now, assume that, $a=s$ and $b=t$, then we get the solution,
$$a=s, \quad b=t, \quad c=\frac{4}{3}t$$
that is, $v=(s,t,\frac{4}{3}t)=s(1,0,0)+t(0,1,\frac{4}{3})$
Hence, all the vectors spanned by the vectors $\{(1,0,0),(0,1,\frac{4}{3})\}$ are orthogonal to $u$.
