If $\pi / 3$ is the angle between the straight lines $p x+q y+r=0$ and $x \sin \alpha+y \cos \alpha=r(r \neq 0)$ which meet at a point $A$ and the straight line $x \cos \alpha-y \sin \alpha=0$ also passes through the point $A$, then

The distance between the point $(2,1)$ and the image of the point $(3,-1)$ with respect to the line $2 x+y-1=0$ is

Let $O A B C$ be a parallelogram. The equation of one diagonal $A C$ is $x+y-1=0$ and the combined equation of the sides $O A, O C$ is $2 x^2-y^2=0$. If $G$ is centroid of the triangle $O A C$, then $B G=$

The acute angle between the pair of straight lines joining the origin to the points of intersection of the line $x+y-1=0$ with the pair of straight lines $k x^2+8 x y-3 y^2+2 x-4 y-1=0$ is