Question

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

• A. $\frac{8}{\sqrt{30}}\hat{i}-\frac{40}{\sqrt{30}}\hat{j}+\frac{16}{\sqrt{30}}\hat{k}$
• B. $\frac{16}{\sqrt{30}}\hat{i}+\frac{8}{\sqrt{30}}\hat{j}-\frac{40}{\sqrt{30}}\hat{k}$
• C. $\frac{40}{\sqrt{30}}\hat{i}-\frac{8}{\sqrt{30}}\hat{j}+\frac{16}{\sqrt{30}}\hat{k}$
• D. None

Answer 1

The correct option is C $\frac{40}{\sqrt{30}}\hat{i}-\frac{8}{\sqrt{30}}\hat{j}+\frac{16}{\sqrt{30}}\hat{k}$

$5\hat{i}-\hat{j}+2\hat{k}$
Unit vector $=\frac{5\hat{i}-\hat{j}+2\hat{k}}{\sqrt{(5{)}^2+(-1{)}^2+(2{)}^2}}$

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

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

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

Hence the answer is $=\frac{40}{\sqrt{30}}\hat{i}-\frac{8}{\sqrt{30}}\hat{j}+\frac{16}{\sqrt{30}}\hat{k}.$