Question

Find the direction cosines of the vector $6\hat{i}+2\hat{j}-3\hat{k}$.

Answer 1

Let $\overrightarrow{r}=6\hat{i}+2\hat{j}-3\hat{k}$
The direction ratios of $\overrightarrow{r}$ are $6,2,-3$
The direction cosines of the given vector are
$\frac{6}{\sqrt{6^2+2^2+{(-3)}^2}},\frac{2}{\sqrt{6^2+2^2+{(-3)}^2}},\frac{-3}{\sqrt{6^2+2^2+{(-3)}^2}}$
$=\frac{6}{\sqrt{49}},\frac{2}{\sqrt{49}},\frac{-3}{\sqrt{49}}$
$=\frac{6}{7},\frac{2}{7},\frac{-3}{7}$