Mathematics

Problem

Consider the vectors

\mathbf{p}=(k,4,-2)

and

\mathbf{q}=(-3,-12,6)

. (i) Determine all real values of

k

for which the two vectors are parallel. (ii) For the value(s) of

k

found in part (i), write

\mathbf{q}

\lambda\mathbf{p}

and hence obtain the corresponding unit vector in their common direction. a. Find all

k\in\mathbb{R}

such that

\mathbf{p}

and

\mathbf{q}

are parallel. b. For each permissible

k

, express

\mathbf{q}=\lambda\mathbf{p}

and then obtain a unit vector in the common direction.