The equation of the plane passing through the points $$(2,3,1),(4,-5,3)$$ and parallel to $$X$$-axis is

The equation of the plane which passes through (2, $$-$$3, 1) and is normal to the line joining the points (3, 4, $$-$$1) and (2, $$-$$1, 5) is given by

If $$G(3,-5, r)$$ is the centroid of $$\triangle A B C$$, where $$A \equiv(7,-8,1), B \equiv(p, q, 5), C \equiv(q+1,5 p, 0)$$ are vertices of the triangle $$A B C$$, then the values of $$p, q, r$$ are respectively

If the lines $$\frac{2 x-4}{\lambda}=\frac{y-1}{2}=\frac{z-3}{1}$$ and $$\frac{x-1}{1}=\frac{3 y-1}{\lambda}=\frac{z-2}{1}$$ are perpendicular to each other, then $$\lambda=$$