A spacecraft thruster exerts a force on space debris given by F_ SD =k , +4 , -2

MATHEMATICS · Multi-part · A Level · Mathematics · Vectors · Vectors

Problem

A spacecraft thruster exerts a force on space debris given by

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

where

k

is a positive constant. (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

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

\vec F_{DS}

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