Question

Write the direction cosines of the vectors \[- 2 \hat{i} + \hat{j} - 5 \hat{k}\].

Answer 1

Given: \[- 2 \hat{i} + \hat{j} - 5 \hat{k}\].
Then, its direction cosines are:
\[\frac{- 2}{\sqrt{\left( - 2 \right)^2 + 1^2 + \left( - 5 \right)^2}} , \frac{1}{\sqrt{\left( - 2 \right)^2 + 1^2 + \left( - 5 \right)^2}} , \frac{- 5}{\sqrt{\left( - 2 \right)^2 + 1^2 + \left( - 5 \right)^2}}\]
 or, \[\frac{- 2}{\sqrt{30}} , \frac{1}{\sqrt{30}} , \frac{- 5}{\sqrt{30}}\]