Find a vector in the direction of vector

Let $\vec{a}=5 \hat{i}-\hat{j}+2 \hat{k} .$

$\therefore|\vec{a}|=\sqrt{5^{2}+(-1)^{2}+2^{2}}=\sqrt{25+1+4}=\sqrt{30}$

$\therefore \hat{a}=\frac{\vec{a}}{|\vec{a}|}=\frac{5 \hat{i}-\hat{j}+2 \hat{k}}{\sqrt{30}}$

Hence, the vector in the direction of vector $5 \hat{i}-\hat{j}+2 \hat{k}$ which has magnitude 8 units is given by,

$8 \hat{a}=8\left(\frac{5 \hat{i}-\hat{j}+2 \hat{k}}{\sqrt{30}}\right)=\frac{40}{\sqrt{30}} \hat{i}-\frac{8}{\sqrt{30}} \hat{j}+\frac{16}{\sqrt{30}} \hat{k}$

$=8\left(\frac{5 \vec{i}-\vec{j}+2 \vec{k}}{\sqrt{30}}\right)$

$=\frac{40}{\sqrt{30}} \vec{i}-\frac{8}{\sqrt{30}} \vec{j}+\frac{16}{\sqrt{30}} \vec{k}$