If (2,3,4) is the centroid of the  tetrahedron for which (2,3,-1), (3,0,-2), (-1,4,3) are three vertices then the fourth vertex is

The centroid of the triangle formed by the points (2,3,-1), (5,6,3),(2,-3,1) is

The locus of a point P such that the distances from P to the points (2,3,5) ,( 1,2,-1)  are in the ratio 5:2 is

The locus of the point if the join of the points (-4,2,3), (2,-1,5) subtends a right angle at P is

The centroid of the tetrahedron formed by the points(3,2,5), (-3,8,-5), (-3,2,1),(-1,4,-3) is

In ABC where A(4,5,6), B(3,2,1), C(5,4,3), if p,q,r are lengths of the medians through A,B,C then ascending order of p,q,r is

A plane passes through (2, 3, -1) and is perpendicular to the line having direction ratios ( 3, -4, 7). The perpendicular distance from the origin to this plane is

The ratio in which (5,4,-6) divides the line segment joining (3,2,-4),(9,8,-10) is

The circumcentre of the triangle formed by the points(1,2,3), (3,-1,5), (4,0,-3) is

The coplanar points(3,2,1), (5,6,5),(2,1,2),(0,-3,-2) form a