Find the direction cosines of the line r= (-2 i+5 2 j-k )+ (2 i+3… - Vidyadip

Question

Find the direction cosines of the line $\bar{r}=\left(-2 \hat{i}+\frac{5}{2} \hat{j}-\hat{k}\right)+\lambda(2 \hat{i}+3 \hat{j})$.

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Answer

The line $\bar{r}=\left(-2 \hat{i}+\frac{5}{2} \hat{j}-\hat{k}\right)+\lambda(2 \hat{i}+3 \hat{j})$ is

parallel to $\bar{b}=2 \hat{i}+3 \hat{j}$.

$\therefore$ direction ratios of the line are $2,3,0$.

$\therefore$ direction cosines of the line are

$\frac{2}{\sqrt{2^2+3^2+0}}, \frac{3}{\sqrt{2^2+3^2+0}}, 0$

i.e. $\frac{2}{\sqrt{13}}, \frac{3}{\sqrt{13}}, 0$.

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