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 \[\stackrel\frown{r}\] 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,
\[\frac{6}{7}, \frac{- 2}{7}, \frac{3}{7}\]