Vector u has its initial point at (-7, 2) and its terminal point at (11, -5). Vector v has a direction opposite that of vector u, and its magnitude is three times the magnitude of u. What is the component form of vector v?

[tex]\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}\\\\ -------------------------------[/tex]

[tex]\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}}[/tex]