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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