Answer
No two are perpendicular.
${\bf u}$ and ${\bf w}$ are parallel.
Work Step by Step
Two vectors are perpendicular if their dot product is zero.
Two vectors are parallel if their cross product is the zero vector.
${\bf u}$ = $\langle 5,-1,1\rangle,\quad {\bf v}$= $\langle 0,1,-5\rangle,\quad {\bf w}$= $\langle-15,3,-3\rangle$
${\bf u}\cdot{\bf v}=5(0)+(-1)(1)+(1)(-5)=-6\neq 0$
${\bf u}\cdot{\bf w}=5(-15)+(-1)(3)+(1)(-3)=-81\neq 0$
${\bf v}\cdot{\bf w}=0(-15)+(1)(3)+(-5)(-3)=-11\neq 0$
No two are perpendicular.
${\bf u}\times{\bf v}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
5 & -1 & 1\\
0 & 1 & -5
\end{array}\right|=(5-1){\bf i}....\neq{\bf 0}$
${\bf u}\times{\bf w}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
5 & -1 & 1\\
-15 & 3 & -3
\end{array}\right|$
$=(3-3){\bf i}-(-15+15){\bf j}+(15-15){\bf k}$
$= {\bf 0}$
${\bf v}\times{\bf w}=\left|\begin{array}{lll}
{\bf i} & {\bf j} & {\bf k}\\
0 & 1 & 5\\
-15 & 3 & -3
\end{array}\right|$
$=(-3-15){\bf i}....\neq{\bf 0}$
${\bf u}$ and ${\bf w}$ are parallel.
