$\bf u\implies 
\begin{cases}
(-7,2)\\
(11,5)
\end{cases}\implies [11-(-7)]~,~[5-2]\implies (11+7)~,~(5-2)
\\\\\\
\stackrel{\textit{component form}}{\ \textless \ 18~,~3\ \textgreater \ }\\\\
-------------------------------\\\\
||u||=\sqrt{18^2+3^2}\implies ||u||=\sqrt{333}\implies ||u||=\sqrt{9\cdot 37}
\\\\\\
||u||=\sqrt{3^2\cdot 37}\implies ||u||=3\sqrt{37}\\\\
-------------------------------$

$\bf \ \textless \ -18~,~-3\ \textgreater \ \impliedby \textit{opposite vector to \underline{u}}
\\\\\\
3\cdot 3\sqrt{37}\implies 9\sqrt{37}\impliedby \textit{3 times the magnitude of \underline{u}}
\\\\\\
3\ \textless \ -18,-3\ \textgreater \ \implies \stackrel{\textit{component form of "v"}}{\ \textless \ -54~,~-9\ \textgreater \ }\impliedby \textit{3 times as long as \underline{u}}$

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3 years ago

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