If $\theta$ is the acute angle between the tangents drawn from the point $(1,1)$ to the hyperbola $4 x^2-5 y^2-20=0$, then $\tan \theta=$

If $A(2,-1,1), B(2,5,1)$ and $C(0,-2,3)$ are the vertices of a triangle. If $D$ is the point of intersection of the side $B C$ and the internal angular bisector of angle $A$, then $A D=$

A line segment $P Q$ has the length 63 and direction ratios $(3,-2,6)$. If this line makes an obtuse angle with $X$-axis, then the components of the vector $\mathbf{P Q}$ are

A plane $\pi$ given by $a x+b y+11 z+d=0$ is perpendicular to the planes $2 x-3 y+z=4$, $3 x+y-z=5$ and the perpendicular distance from the origin to the plane $\pi$ is $\sqrt{6}$ units. If all the intercepts made by the plane $\pi$ on the coordinate axes are positive, then $d=$