\begin{align*}
\color{blue}\mathbf{u}~ &\color{blue}= \langle -1,~~~2,~~~4 \rangle \\
\color{red}\mathbf{v}~ &\color{red}= \langle ~~~2,~~~3,~~~2 \rangle \\ \\
\color{black}\mathbf{u}\cdot\mathbf{v}~ &\color{black}= u_1v_1 + u_2v_2 + u_3v_3 \\
&\color{black}= \color{blue}(-1)\color{red}(2) + \color{blue}(2)\color{red}(3) + \color{blue}(4)\color{red}(2) \\
&\color{black}= \boxed{12}
\end{align*}
\begin{align*}
\color{blue}|\mathbf{u}|~ &\color{blue}= \sqrt{21} \approx 4.583 \\
\color{red}|\mathbf{v}|~ &\color{red}= \sqrt{17} \approx 4.123 \\ \\
\color{black}\mathbf{u}\cdot\mathbf{v}~ &\color{black}= \color{blue}|\mathbf{u}|\color{red}|\mathbf{v}|\color{black}\cos\theta \\
&\color{black} \approx \color{blue}(4.583)\color{red}(4.123)\color{black}(0.688) \\
&\color{black} \approx \boxed{11.999}
\end{align*}