The angle between the lines $\bar{r}=(3 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(\hat{i}+2 \hat{j}+2 \hat{k})$ and $\bar{r}=(5 \hat{i}-2 \widehat{k})+\mu(3 \hat{i}+2 \hat{j}+6 \widehat{k})$

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Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Required angle }=\cos ^{-1}\left(\frac{(\hat{i}+2 \hat{j}+2 \widehat{k}) \cdot(3 \hat{i}+2 \hat{j}+6 \hat{k})}{\sqrt{1^2+2^2+2^2} 	imes \sqrt{3^2+2^2+6^2}}ight) \ & {\left[\because 	heta=\cos ^{-1}\left(\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}ight)ight]} \ & =\cos ^{-1}\left(\frac{1 	imes 3+2 	imes 2+2 	imes 6}{3 	imes 7}ight) \ & =\cos ^{-1}\left(\frac{19}{21}ight)\end{aligned}$

The angle between the lines $\bar{r}=(3 \hat{i}+2 \hat{j}-4 \hat{k})+\lambda(\hat{i}+2 \hat{j}+2 \hat{k})$…

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