If the centroid of tetrahedron OABC where A ,B, C are given by (a, 2, 3) ,(1 ,b, 2) and (2, 1, c) respectively is (1, 2, -1) then distance of P(a, b, c) from origin is

If the centroid of tetrahedron OABC where A,B,C are given by (a,2,3),(1,b,2) and (2,1,c) respectively is (1,2,−2), then distance of P(a,b,c) from origin is

If the centroid of the tetrahedron OABC where A,B,C are the points (a,2,3),(1,b,2) and (2,1,c) be (1,2,3) and the point (a,b,c) is at distance 5sqrt(lambda) from origin then lambda^(2) must be equals to

Centroid of the tetrahedron OABC, where A=(a,2,3) , B=(1,b,2) , C=(2,1,c) and O is the origin is (1,2,3) the value of a^(2)+b^(2)+c^(2) is equal to:

If the centroid of the tetrahedron O-ABC, where A-=(alpha,5,6), B-=(1,beta,4) and C-=(3,2,gamma) is G(1,-1,2) , then: alpha^(2) + beta^(2) + gamma^(2)=

lf origin is centroid of triangle with vertices (a, 1 , 3), (- 2, b, -5) and (4, 7, c), then (a, b, c) equiv

The volume of the tetrahedron whose vertices are A(-1, 2, 3), B(3, -2, 1), C(2, 1, 3) and C(-1, -2, 4)

(i) A variable plane, which remains at a constant distance '3p' from the origin cuts the co-ordinate axes at A, B, C. Show that the locus of the centroid of the triangle ABC is : (1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (1)/(p^(2)) . (ii) A variable is at a constant distance 'p' from the origin and meets the axes in A, B, C respectively, then show that locus of the centroid of th triangle ABC is : (1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (9)/(p^(2)).

Distance of point A(1,4,-2) is the distance from BC, where B and C The coordinates are respectively (2,1,-2) and (0,-5,1) respectively