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Question
Find the direction cosines of the following vectors:
\[2 \hat{i} + 2 \hat{j} - \hat{k}\]
Solution
We have,
\[2 \hat{i} + 2 \hat{j} - \hat{k}\]
The direction cosines are
\[\frac{2}{\sqrt{2^2 + 2^2 + \left( - 1 \right)^2}}, \frac{2}{\sqrt{2^2 + 2^2 + \left( - 1 \right)^2}} , \frac{- 1}{\sqrt{2^2 + 2^2 + \left( - 1 \right)^2}}\]
or,
\[\frac{2}{3} , \frac{2}{3} , \frac{- 1}{3}\]
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