Equation of plane containing the line $$\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$$ and perpendicular to the plane containing the lines $$\frac{x}{3}=\frac{y}{4}=\frac{z}{2}$$ and $$\frac{x}{4}=\frac{y}{2}=\frac{z}{3}$$ is

The centroid of tetrahedron with vertices at $$\mathrm{A}(-1,2,3), \mathrm{B}(3,-2,1), \mathrm{C}(2,1,3)$$ and $$\mathrm{D}(-1,-2,4)$$ is

A plane is parallel to two lines whose direction ratios are $$1,0,-1$$ and $$-1,1,0$$ and it contains the point $$(1,1,1)$$. If it cuts the co-ordinate axes at $$\mathrm{A}, \mathrm{B}, \mathrm{C}$$, then the volume of the tetrahedron $$\mathrm{OABC}$$ (in cubic units) is

The equation of the plane through $$(-1,1,2)$$ whose normal makes equal acute angles with co-ordinate axes is