Question

Given vectors u = (-3,2) and v = (4,-1), if vector w=2u -3v, what is ||w|| ?

Answer 1

$\bf \begin{cases} u=\ \textless \ -3,2\ \textgreater \ \\ 2u=2\ \textless \ -3,2\ \textgreater \ \\ \qquad \ \textless \ 2\cdot -3,2\cdot 2\ \textgreater \ \\ \qquad \boxed{\ \textless \ -6,4\ \textgreater \ }\\ ----------\\ v=\ \textless \ 4,-1\ \textgreater \ \\ 3v=3\ \textless \ 4,-1\ \textgreater \ \\ \qquad \ \textless \ 3\cdot 4,3\cdot -1\ \textgreater \ \\ \qquad \boxed{\ \textless \ 12,-3\ \textgreater \ } \end{cases}\qquad \begin{array}{llll} w=2u-3v\\\\ w=\ \textless \ -6,4\ \textgreater \ -\ \textless \ 12,-3\ \textgreater \ \\\\ w=\ \textless \ -6-12,4-(-3)\ \textgreater \ \\\\ w=\ \textless \ -18,4+3\ \textgreater \ \\\\ \boxed{w=\ \textless \ -18,7\ \textgreater \ } \end{array} \\\\\\ ||w||\implies \sqrt{a^2+b^2}\implies ||w||=\sqrt{(-18)^2+(7)^2}\implies ||w||=373$