Question

Write the direction cosines of the vector $\overrightarrow{r}=6\hat{i}-2\hat{j}+3\hat{k}.$

Answer 1

Given: $\overrightarrow{r}=6\hat{i}-2\hat{j}+3\hat{k}$
Then, direction cosines of $\stackrel{⏜}{r}$ are $\frac{6}{\sqrt{6^2+{\left(-2\right)}^2+3^2}},\frac{-2}{\sqrt{6^2+{\left(-2\right)}^2+3^2}},\frac{3}{\sqrt{6^2+{\left(-2\right)}^2+3^2}}$ or, $\frac{6}{7},\frac{-2}{7},\frac{3}{7}$