Question

Find a vector parallel to the given vector $5\hat{i}-\hat{j}+2\hat{k}$ which has magnitude $8$ units.

Answer 1

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

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

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

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

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