Mathematics

Problem

The magnitude of a vector

\mathbf{q}

is given to be

k>0

. Its direction cosines are proportional to

1:2:-2

. (i) Express the three direction cosines in terms of a single variable and determine their numerical values. (ii) Hence write

\mathbf{q}

in component form in terms of

k

. (iii) Obtain the unit vector in the direction of

\mathbf{q}