Question

Which could be the initial point of vector u if it has a magnitude of 17 and the terminal point (3,13)?

Answer 1

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -5 &,& -2~) % (c,d) &&(~ 3 &,& 13~) \end{array}\\\\\\ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ ||u||=\sqrt{[3-(-5)]^2+[13-(-2)]^2}\implies ||u||=\sqrt{(3+5)^2+(13+2)^2} \\\\\\ ||u||=\sqrt{64+225}\implies ||u||=\sqrt{289}\implies ||u||=17$