Question

Given p = (6,6) and q = (-5,- 3) find the magnitude of 2p + 3q

A. 2√3
B. 3√2
C.√144
D.14

Answer 1

`\begin{cases} p= < 6,6 > \\ q= < -5,-3 > \end{cases}\qquad \qquad \stackrel{2p}{2 < 6,6 > }~~ + ~~\stackrel{3q}{3 < -5,-3 > } \\\\\\ \stackrel{2p}{ < (2)(6)~~,~~(2)(6) > }~~ + ~~\stackrel{3q}{ < (3)(-5)~~,~~(3)(-3) > } \\\\\\ < 12~~,~~12 > ~~ + ~~ < -15~~,~~-9 > \implies < 12-15~~,~~12-9 > \\\\\\ \stackrel{2p~~ + ~~3q}{\boxed{ < -3~~,~~3 > }}\qquad \qquad ||\stackrel{magnitude}{ < -3,3 > }||\implies √((-3)^2 + (3)^2)\implies 3√(2)`