The locus of a point P such that PA+PB=4 where A=(2,3,4) ,B=(-2,3,4) is

If the orthocenter and the circumcentre of a triangle are (-3,5,2), (6,2,5) then its centroid is

The ends of the hypotenuse of a right angled triangle are (2,0,-3), (0,4,1) then the locus of the third vertex is

The line joining the points (2,3,4) and (4,10,7) intersects the line joining(2,-1,5) and (4, -30,17). Then the coordinates of the point of intersection are

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

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

The points of trisection of the line segment joining (2,-3,5), (3,1,-2) are

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

The locus of a point which is at a distance of 5 unit from (2,1,-3) is

The distance between the circumcentre and the orthocenter of the triangle formed by the points (2,1,5), (3,2,3), (4,0,4) is