Question

If $\overrightarrow{a}=\hat{i}+\hat{j}+2\hat{k}\text{and}\overrightarrow{b}=2\hat{i}+\hat{j}+2\hat{k},$ then find the unit vector in the direction of 6 $\overrightarrow{b}$

Answer 1

Here, $\overrightarrow{a}=\hat{i}+\hat{j}+2\hat{k}\text{and}\overrightarrow{b}=2\hat{i}+\hat{j}+2\hat{k},$

Since, $6\overrightarrow{b}=12\hat{i}+6\hat{j}-12\hat{k}$

$\therefore$ Unit vector in the direction of $6\overrightarrow{b}=\frac{6\overrightarrow{b}}{|6\overrightarrow{b}|}=\frac{12\hat{i}+6\hat{j}-12\hat{k}}{\sqrt{{12}^2+6^2+{12}^2}}=\frac{6(2\hat{i}+\hat{j}-2\hat{k})}{\sqrt{324}}=\frac{6(2\hat{i}+\hat{j}-2\hat{k})}{18}=\frac{2\hat{i}+\hat{j}-2\hat{k}}{3}$