The angle between the line \(\bar{r} = (\hat{i} + 2\hat{j} + \hat{k}) + \lambda(\hat{i} + \hat{j} + \hat{k})\) and the plane \(\bar{r}\cdot(2\hat{i} - \hat{j} + \hat{k}) = 8\) is _____.
Q.1 (iv) The angle between the line \(\bar{r} = (\hat{i} + 2\hat{j} + \hat{k}) + \lambda(\hat{i} + \hat{j} + \hat{k})\) and the plane \(\bar{r}\cdot(2\hat{i} - \hat{j} + \hat{k}) = 8\) is _____.
A. \(\sin^{-1}\left(\dfrac{\sqrt{2}}{3}\right)\)
B. \(\sin^{-1}\left(\dfrac{\sqrt{3}}{2}\right)\)
C. \(\sin^{-1}\left(\dfrac{1}{2}\right)\)
D. \(\sin^{-1}\left(\dfrac{1}{\sqrt{2}}\right)\)