If $e_1$ is the eccentricity of the hyperbola $x=\sec \theta$, $y=\sqrt{2} \tan \theta$ and $e_2$ is the eccentricity of the hyperbola $x=\sqrt{2} \sec \theta$ and $y=\tan \theta$, then $\frac{e_2^2}{e_1^2}=$

$A(27,-243,81)$ is a point in space, $B, C$ and $D$ are images of $A$ with respect to $X Y, Y Z$ and $Z X$ planes respectively. If the centroid of the $\triangle B C D$ is $(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma=$

Let $A(2,5,7)$ be the image of the point $B(1,-2,3)$ with respect to a plane $\pi$. Let $C$ be the point where $A B$ meets the plane $\pi$. Let $D=(2,1,6)$. Then, the direction cosines of $C D$ are

If a plane $x+y+z-5=0$ intersects the line joining $A(1,1,1)$ and $B(2,2,2)$ at $P$, then $A P: P B=$