Question
Find the angle between the lines $\bar{r}=3 \hat{i}+2 \hat{j}-4 \widehat{k}+\lambda(\hat{i}+2 \hat{j}+2 \widehat{k})$ and $\bar{r}=5 \hat{i}-2 \widehat{k}+\mu(3 \hat{i}+2 \hat{j}+6 \widehat{k})$
✓
Answer
Let $\bar{b}_1$ and $\bar{b}_2$ be the vectors in the direction of the lines
Let θ be the acute angle between the two given lines.
$\therefore \cos \theta=\frac{\bar{b}_1 \bar{b}_2}{\left|\bar{b}_1\right|\left|\bar{b}_2\right|}=\frac{19}{3 \times 7}$
$\therefore \cos \theta=\frac{19}{21}$
$\theta=\cos ^{-1}\left(\frac{19}{21}\right)$
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