Answer
\[
(\vec{v} \times \vec{w})\cdot\vec{u} =-3
\]
Work Step by Step
To evaluate $ (\vec{w} \times \vec{v})\cdot\vec{u}$, we can use the following formula.
\[
(\vec{w} \times \vec{v})\cdot \vec{u} =\left|\begin{array}{lll}
u_{1} & u_{2} & u_{3} \\
v_{1} & v_{2} & v_{3} \\
w_{1} & w_{2} & w_{3}
\end{array}\right|
\]
It's given that
\[
\vec{w}=\langle 4,0,1\rangle , \vec{v}=\langle 1,-3,1\rangle \text { and } \vec{u}=\langle 2,1,0\rangle
\]
And then,
\[
\begin{aligned}
(\vec{w} \times \vec{v})\cdot\vec{u} &=\left|\begin{array}{rrr}
2 & 1 & 0 \\
1 & -3 & 1 \\
4 & 0 & 1
\end{array}\right| \\
&=2\left|\begin{array}{cc}
-3 & 1 \\
0 & 1
\end{array}\right|-(1)\left|\begin{array}{cc}
1 & 1 \\
4 & 1
\end{array}\right|+0\left|\begin{array}{cc}
1 & -3 \\
4 & 0
\end{array}\right|
\end{aligned}
\]
\[
-3=(\vec{w} \times \vec{v})\cdot \vec{u}
\]
