• # question_answer If the angle between the plane $x-3y+2z=1$ and the line $\frac{x-1}{2}=\frac{y-1}{1}=\frac{z-1}{-3}$ is $\theta$, then the value of $\cos ec\theta$ is A)  1                     B)  2 C)  3                                 D)  4

Vector normal to the plane is $\vec{n}=\hat{i}-3\hat{j}+2\hat{k}$ and  vector along the line is $\vec{V}=2\hat{i}+\hat{j}-3\hat{k}$ Now $\sin \theta =\frac{n.v}{|n||v|}\,=\left| \frac{2-3-6}{\sqrt{14}\,\sqrt{14}} \right|\,=\left| \frac{7}{14} \right|$ Hence $\cos ec\,\theta =2$