Chapter 5 - Inner Product Spaces - Review Exercises - Page 284: 24

$v=(r,s,t,s+2t)$

Let $u=(0,1,2,-1)$ and $v=(a,b,c,d)$ such that $u$ is orthogonal to $v$, that is $$u\cdot v=0 \Longrightarrow b+ 2c-d=0.$$ Now, assume that, $a=r$ and $b=s$, $c=t$ then we get the solution, $$a=r, \quad b=s, \quad c=t,\quad d=s+2t$$ that is, $v=(r,s,t,s+2t)$ Thus all such vectors are orthogonal to $u$.