Find the equation of the plane passing through the point $$(2,1,3)$$ and perpendicular to the planes $$x-2 y+2 z+3=0$$ and $$3 x-2 y+4 z-4=0$$.

The ratio in which the YZ-plane divides the line joining (2, 4, 5) and (3, 5, $$-$$4) is

The direction cosines of a line which makes equal angles with the coordinate axes are

Let $$O$$ be the origin and $$P$$ be a point which is at a distance of 3 units from the origin. If the direction ratios of $$\overline{O P}$$ are $$(1,-2,-2)$$, then the coordinates of $$P$$ are