Introduction to...

If O and O' are circumcenter and orthocenter of a $$\Delta ABC$$ where $$\overline{OA} + \overline{OB} + \overline{OC}$$ is $$\lambda \overline{OO'}$$ then the value of $$\lambda$$ is

The distance between the orthocentre and circumcentre of the triangle formed by the points $$(1, 2, 3), (3, -1, 5), (4, 0, -3)$$ is

If $$R$$ divides the line segment joining $$P(2,3,4)$$ and $$Q(4,5,6)$$ in the ratio $$-3:2$$, then the parameter which represent $$R$$ is 

In the $$xy-plane$$, the length of the shortest from $$(0, 0)$$ to $$(12, 16)$$ that does not go inside the circle $$(x - 6)^{2} + (y + 8)^{2} = 25$$ is

Consider at three dimensional figure represented by $$xy{ z }^{ 2 }=2$$, then its minimum distance from origin is

Perpendicular distance from the origin to the line joining the points $$(a\cos{\theta},a\sin{\theta})(a\cos{\theta},a\sin{\theta})$$ is

Q, R, S are the points $$(-2, -1), (0, 3) (4, 0)$$ respectively. Then the coordinates of P such that PQRS is a parallelogram is ________________.

The point which is equidistant from the points $$(-1,1,3),(2,1,2),(0,5,6)$$ and $$(3,2,2)$$ is

Minimum distance between the curves
$$y^{2}=4x$$ & $$x^{2}+y^{2} -12x+31=0$$ is -