Question

Vector u has its initial point at (17, 5) and its terminal point at (9, -12). Vector v has its initial point at (12, 4) and its terminal point at (3, -2). Find ||3u − 2v||. Round your answer to the nearest hundredth.

Answer 1

`\bf \vec{u}~~ \begin{cases} (17,5)\\ (9,12) \end{cases}\implies <9-17~,~12-5>\implies \stackrel{\textit{component form}}{<-8~,~7>} \\\\\\ \vec{v}~~ \begin{cases} (12,4)\\ (3,-2) \end{cases}\implies <3-12~,~-2-4>\implies \stackrel{\textit{component form}}{<-9~,~-6>} \\\\[-0.35em] ~\dotfill`

`\bf 3\vec{u}\implies 3<-8,7>\implies <-24,21> \\\\\\ 2\vec{v}\implies 2<-9,-6>\implies <-18,-12> \\\\\\ 3\vec{u}-2\vec{v}\implies <-24,21>-<-18,-12>\implies <-24,21>+<18,12> \\\\\\ <-24+8~,~21+12>\implies <-16,33> \\\\[-0.35em] ~\dotfill\\\\ ||3\vec{u}-2\vec{v}||\implies ||<-16,33>||\implies √((-16)^2+33^2) \\\\\\ √(1345)\implies 36.67`