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)=

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 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 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

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)

If the line (x-1)/(2)=(y-2)/(3)=(z-4)/(4) intersect the xy and yz plane at points A and B respectively. If the volume of the tetrahedron OABC is V cubic units (where, O is the origin) and point C is (1, 0, 4), then the value of 102V is equal to

If a,b,c are positive real numbers and 2a+b+3c=1 , then the maximum value of a^(4)b^(2)c^(2) is equal to