Question

Given that P = (-9, 2) and Q = (-10, 9), find the component form and magnitude of 2vector PQ.

Answer 1

$\bf \begin{array}{lllllll} (&-9,&2),(&-10,&9)\\ &x_1&y_1&x_2&y_2 \end{array}\implies \ \textless \ x_2-x_1\ ,\ y_2-y_1\ \textgreater \ \leftarrow \begin{array}{llll} component\\ form \end{array} \\\\\\ \ \textless \ -10-(-9)\ ,\ 9-2\ \textgreater \ \implies \ \textless \ -1,7\ \textgreater \ \impliedby PQ\\\\ -------------------------------\\\\ 2PQ\implies 2\ \textless \ -1,7\ \textgreater \ \implies \ \textless \ 2\cdot -1,2\cdot 7\ \textgreater \ \implies \begin{array}{rllll} \ \textless \ -2&,&14\ \textgreater \ \\ a&&b \end{array} \\\\\\ magnitude\qquad \sqrt{a^2+b^2}\implies \sqrt{(-2)^2+(14)^2}\implies \sqrt{200} \\\\\\ 10\sqrt{2}$