Mathematics

Problem

A spacecraft thruster exerts a force on space debris given by

\vec F_{SD}=k\,\hat i+4\,\hat j-2\,\hat k\,\text{N},

where

k

is a positive constant. a. (i) If the debris exerts a reaction force on the spacecraft whose magnitude is

\lvert\vec F_{DS}\rvert=9\,\text{N}

, find the value of

k

. b. (ii) Write the full vector for the force on the spacecraft,

\vec F_{DS}

. c. (iii) Show that the two forces obtained are collinear but oppositely directed.