If the coordinates of the vertices of $\Delta OAB$ are $(0, 0)$,$(\cos \alpha, \sin \alpha)$,and $(-\sin \alpha, \cos \alpha)$ respectively,then $OA^2 + OB^2 = $

What is the distance between the points $(2, 15^{\circ})$ and $(1, 75^{\circ})$ in polar coordinates?

The point $A$ divides the join of the points $(-5, 1)$ and $(3, 5)$ in the ratio $k : 1$. The coordinates of the points $B$ and $C$ are $(1, 5)$ and $(7, -2)$ respectively. If the area of the triangle $ABC$ is $2$ square units,then $k =$

If the line $2x - y - 4 = 0$ divides the line segment joining the points $(2, -1)$ and $(1, -4)$ at the point $(a, b)$ in the ratio $m:n$,then $4(a - b(\frac{m}{n})^2) = $

The point which divides externally the line joining the points $(a + b, a - b)$ and $(a - b, a + b)$ in the ratio $a:b$ is

If the Cartesian coordinates of a point are $(\sqrt{3}, 1)$,find its polar coordinates.