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Let $\mathbf{v} = \begin{pmatrix} -4.6 \\ 23.6 \\ -5.6 \end{pmatrix}$. Find $|\mathbf{v}|$.
Hint: Square the components, add the results together, then take the square root.
$\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A1}}\hspace{54px}}~} {}^2 + \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A2}}\hspace{54px}}~} {}^2 + \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A3}}\hspace{54px}}~} {}^2$ $-4.6 {}^2 + 23.6 {}^2 + -5.6 {}^2$
$= \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B1}}\hspace{54px}}~} + \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B2}}\hspace{54px}}~} + \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B3}}\hspace{54px}}~} = \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{BR}}\hspace{54px}}~}$ $= 21.16 + 556.96 + 31.36 = 609.48$
Therefore,
$|\mathbf{v}| = \sqrt{\class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{C1}}\hspace{54px}}~}} = \class{inputBox step3}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{CR}}\hspace{54px}}~}$ $|\mathbf{v}| = \sqrt{609.48} = 24.68764873$