Find the direction cosines of the vector 2 i+2 i-k - Vidyadip

Question

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

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Answer

Let $|\vec{a}|=2 \hat{i}+2 \hat{j}-\hat{k}$
$
\begin{aligned}
& \therefore|\bar{a}|=\sqrt{(2)^2+(2)^2+(-1)^2}=\sqrt{9}=3 \\
\therefore & \hat{a}=\frac{\bar{a}}{|\bar{a}|}=\frac{2 \hat{i}+2 \hat{j}+\hat{k}}{3}=\frac{2}{3} \hat{i}+\frac{2}{3} \hat{j}-\frac{1}{3} \hat{k}
\end{aligned}
$
$\therefore \quad$ The direction cosines of $\bar{a}$ are $\frac{2}{3}, \frac{2}{3},-\frac{1}{3}$

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