If $f(\theta)=\cos \theta_1 \cdot \cos \theta_2 \cdot \cos \theta_3$ .............. $\cos \theta_n$, then $\tan \theta_1+\tan \theta_2+\tan \theta_3+$. ............ $+\tan \theta_{\mathrm{n}}=$

The length of the altitude through the point $D$ of tetrahedron where the vertices of the tetrahedron are $A(2,3,1), B(4,1,-2), C(6,3,7), D(-5,-4,8)$, is

The angle between the lines $\frac{x-1}{l}=\frac{y+1}{m}=\frac{z}{n}$ and $\frac{x+1}{\mathrm{~m}}=\frac{y-3}{\mathrm{n}}=\frac{\mathrm{z}-1}{l}$, where $l>\mathrm{m}>\mathrm{n}$ and $1, \mathrm{~m}, \mathrm{n}$ are roots of the equation $x^3+x^2-4 x-4=0$, is

The distance of the point $\mathrm{P}(3,8,2)$ from the line $\frac{x-1}{2}=\frac{y-3}{4}=\frac{z-2}{3}$ measured parallel to the plane $3 x+2 y-2 z+15=0$ is