Question

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

Answer 1

Given $\overrightarrow{r}=(6\hat{i}+2\hat{j}-3\hat{k})$

The direction ratios of this vector are $6,2,-3$.

The direction cosines are $\frac{6}{\sqrt{6^2+2^2+3^2}},\frac{2}{\sqrt{49}},\frac{-3}{\sqrt{49}}$

$\Rightarrow \pm \frac{6}{7},\pm \frac{2}{7}$