A to Z Exams

If the centroid of the triangle formed by (a,1,3), (-2,b,-5) and (4,7,c) is the origin then(a,b,c)=

If the orthocenter and the circumcentre of a triangle are (-3,5,1), (3,3,-1) then the circumcentre 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

The orthocentre 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(2,1,5), (3,2,3), (4,0,4) is

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

The point dividing the join of (3, -2, 1} and (-2, 3, 11) in the ratio 2 : 3 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 circumradius of the triangle formed by the points (2,-1,1) , (1,-3,-5), (3,-4,-4) is

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

The locus of a point which is equidistant from the points(-2,2,3), (3,4,5) is

The fourth vertex of the parallelogram whose consecutive vertices are (2,4,-1), (3,6,-1),(4,5,1) is

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 ratio in which (5,4,-6) divides the line segment joining (3,2,-4),(9,8,-10) 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 locus of a point which is at a distance of 5 unit from (2,1,-3) 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 centroid of the triangle formed by the points (2,3,-1), (5,6,3),(2,-3,1) is

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

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

The ratio in which yz-plane divides the line segment joining (3,4,5) ,(2,-3,1) is

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

If (2,1,1) is the centroid of the triangle for which (3,2,-1), (2,-2,5) are two vertices then the third vertex 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 fourth vertex of the square whose consecutive vertices are (4,5,1), (2,4,-1), (3,6,-3) is

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

A(0,2,3), B(2,-1,5), C(3,0,-3) are vertices of ABC. If  a,b,c are HG,GS,SH then their ascending order is

If (1,2,3), (2,3,1) are two vertices of an equilateral triangle then its third vertex 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