question_answer

Angle between the line \[\mathbf{r}=(2\mathbf{i}-\mathbf{j}+\mathbf{k})+\lambda (-\mathbf{i}+\mathbf{j}+\mathbf{k})\] and the plane \[\mathbf{r}.(3\mathbf{i}+2\mathbf{j}-\mathbf{k})=4\] is

A)            \[{{\cos }^{-1}}\left( \frac{2}{\sqrt{42}} \right)\]

B)            \[{{\cos }^{-1}}\left( \frac{-2}{\sqrt{42}} \right)\]

C)            \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{42}} \right)\]

D)            \[{{\sin }^{-1}}\left( \frac{-2}{\sqrt{42}} \right)\]