The vector in the direction of the vector $\widehat {\rm{i}} - 2\widehat {\rm{j}} + 2\widehat {\rm{k}}$ that has magnitude 9 is

Let $\overrightarrow {\rm{a}} = \widehat {\rm{i}} - 2\widehat {\rm{j}} + 2\widehat {\rm{k}}$

Any vector in the direction of a vector $\vec a$ is given by $\frac{{\vec a}}{{|\vec a|}}$

.$= \frac{{\widehat {\rm{i}} - 2\widehat {\rm{j}} + 2\widehat {\rm{k}}}}{{\sqrt {{1^2} + {2^2} + {2^2}} }} = \frac{{\widehat {\rm{i}} - 2\widehat {\rm{j}} + 2\widehat {\rm{k}}}}{3}$

$\therefore$ Vector in the direction of $\vec a$ with magnitude

$9 = 9 \cdot \frac{{\widehat {\rm{i}} - 2\widehat {\rm{j}} + 2\widehat {\rm{k}}}}{3}$

$= 3(\widehat {\rm{i}} - 2\widehat {\rm{j}} + 2\widehat {\rm{k}})$