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The plane $$ax+by + cz + d = 0$$ divides the line joining $$(x_1, y_1, z_1)$$ and $$(x_2, y_2, z_2)$$ in the ratio

If the centroid of triangle whose vertices are $$(a, 1, 3), (-2, b, - 5)$$ and $$(4, 7, c)$$ be the origin, then the values of $$a, b$$ and $$c$$ are

Find the ratio in which $$2x + 3y + 5z = 1$$ divides the line joining the points $$(1,\ 0,\ -3)$$ and $$(1,\ -5,\ 7)$$.

If the sum of the squares of the distance of a point from the three coordinate axes be $$36$$, then its distance from the origin is

The circum radius of the triangle formed by the points $$(0, 0, 0)$$, $$(0, 0, 12)$$ and $$(3, 4, 0)$$ is

The coordinates of the point where the line segment joining $$A(5,1,6)$$ and $$B (3,4,1)$$ crosses the yz plane are

Four vertices of a tetrahedron are $$(0, 0, 0), (4, 0, 0), (0, -8, 0)$$ and $$(0, 0, 12)$$. Its centroid has the coordinates

If $$P= (0, 0, 0), Q = (3, 6, 9)$$ and $$R$$ is a point of trisection of $$PQ$$, then $$R_y=$$

If the plane $$7x + 11y+ 13z= 3003$$ meets the axes in $$A, B, C$$, then the centroid of $$\Delta ABC$$ is

Three vertices of a tetrahedron are $$(0, 0, 0), (6, -5, -1) $$ and $$(-4, 1, 3)$$. If the centroid of the tetrahedron be $$(1, -2, 5) $$ then the fourth vertex is