Question

Angle between the lines $\overline{r}=(\hat{i}+2\hat{j}-\hat{k})+\mu (\hat{i}-\hat{j}+\hat{k})$ and Normal to the plane $\overline{r}=(2\hat{i}-\hat{j}+\hat{k})$

• A. $si{n}^{-1}\left(\frac{2\sqrt{2}}{3}\right)$
• B. $co{s}^{-1}\left(\frac{2\sqrt{2}}{3}\right)$
• C. $ta{n}^{-1}\left(\frac{2\sqrt{2}}{3}\right)$
• D. $co{t}^{-1}\left(\frac{2\sqrt{2}}{3}\right)$

Answer 1

The correct option is B $co{s}^{-1}\left(\frac{2\sqrt{2}}{3}\right)$

Angle between the lines $\overline{r}=(\hat{i}+2\hat{j}-\hat{k})+\mu (\hat{i}-\hat{j}+\hat{k})$ and Normal to the plane
$\overline{r}=(2\hat{i}-\hat{j}+\hat{k})=4$
$\theta ={\cos }^{-1}\left[\frac{(\hat{i}-\hat{j}+\hat{k}).(2\hat{i}-\hat{j}+\hat{k})}{\sqrt{(1^2+1^2+1^2)(2^2+1^2+1^2)}}\right]=co{s}^{-1}\left(\frac{2\sqrt{2}}{3}\right)$
Ans: B