Mathematics

Problem

Two forces are represented by the vectors

\mathbf{F}_{1}=\langle 4,\,-3,\,12\rangle

and

\mathbf{F}_{2}=\langle k,\,-\dfrac{3k}{4},\,3k\rangle

. a. (i) Determine the value(s) of

k

for which

\mathbf{F}_{1}

and

\mathbf{F}_{2}

act along the same line. b. (ii) For each value of

k

obtained, decide whether the two forces have the same sense (act in the same direction) or the opposite sense. c. (iii) Compute the magnitude of

\mathbf{F}_{2}

corresponding to each permissible value of

k