The vector equation of the line passing through $$\mathrm{P}(1,2,3)$$ and $$\mathrm{Q}(2,3,4)$$ is

Equation of planes parallel to the plane $$x-2y+2z+4=0$$ which are at a distance of one unit from the point (1, 2, 3) are

The area of triangle with vertices $$(1,2,0),(1,0, a)$$ and $$(0,3,1)$$ is $$\sqrt{6}$$ sq. units, then the values of '$$a$$' are

If $$\mathrm{G}(4,3,3)$$ is the centroid of the triangle $$\mathrm{ABC}$$ whose vertices are $$\mathrm{A}(\mathrm{a}, 3,1), \mathrm{B}(4,5, \mathrm{~b})$$ and $$C(6, c, 5)$$, then the values of $$a, b, c$$ are