Mathematics

Problem

A vector

\vec{v}=2\mathbf{i}+k\mathbf{j}-3\mathbf{k}

is known to have magnitude

7

. (i) Find the possible value(s) of the real number

k

. (ii) For each value of

k

obtained in part (i), write the unit vector in the direction of

\vec{v}

. (iii) Hence determine the direction cosines of

\vec{v}

for each admissible value of

k