Processing math: 16%
u =⟨−1, 2, 4⟩v =⟨ 2, 3, 2⟩u⋅v =u1v1+u2v2+u3v3=(−1)(2)+(2)(3)+(4)(2)=12
\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*}