Find a vector in the direction of vector $5\hat i - \hat j + 2\hat k$ which has magnitude $8$ units.

Let given vector is $\vec a = 5\hat i - \hat j + 2\hat k$
$\therefore$ $|\vec a| = \sqrt {{5^2} + {{( - 1)}^2} + {2^2}} = \sqrt {25 + 1 + 4} = \sqrt {30}$
$\therefore$

Unit vector in the direction of given vector $\vec a$
$= \cfrac{{\vec a}}{{|\vec a|}} = \cfrac{1}{{\sqrt {30} }}(5\hat i - \hat j + 2\hat k)$
$\therefore$

Vector of magnitude $8$ in the direction of vector $\vec a$ $= 8\cfrac{{\vec a}}{{|\vec a|}} = 8\cfrac{1}{{\sqrt {30} }}(5\hat i - \hat j + 2\hat k) = \cfrac{{40}}{{\sqrt {30} }}\hat i - \cfrac{8}{{\sqrt {30} }}\hat j + \cfrac{{i6}}{{\sqrt {30} }}\hat k$