Home
Class 12
MATHS
Let G(1), G(2) and G(3) be the centroid ...

Let `G_(1), G(2) and G_(3)` be the centroid of the triangular faces OBC, OCA and OAB of a tetrahedron OABC. If `V_(1)` denotes the volume of tetrahedron OABC and `V_(2)` that of the parallelepiped with `OG_(1), OG_(2) and OG_(3)` as three concurrent edges, then the value of `(4V_(1))/(V_2)` is (where O is the origin

Text Solution

Verified by Experts

The correct Answer is:
`(9)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the readings V_(1) and V_(3) are 10. volt each, then reading of V_(2) is:

If m is the AM of two distinct real numbers l and n (l,ngt1) and G_(1),G_(2)" and "G_(3) are three geometric means between l and n, then G_(1)^(4)+2G_(2)^(4)+G_(3)^(4) equals

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

The volume of a parallelepiped with edges vec(OA)=(3,1.4),vec(OB)=(1,2,3),vec(OC)=(2,1,5) is ……………

A plenet moving along an elliptical orbit is closest to the sun at a distance r_(1) and farthest away at a distance of r_(2) . If v_(1) and v_(2) are the linear velocities at these points respectively, then the ratio (v_(1))/(v_(2)) is

A plane passing through (1,1,1) cuts positive direction of coordinates axes at A ,Ba n dC , then the volume of tetrahedron O A B C satisfies a. Vlt=9/2 b. Vgeq9/2 c. V=9/2 d. none of these

Statement 1 : Let A(veca), B(vecb) and C(vecc) be three points such that veca = 2hati +hatk , vecb = 3hati -hatj +3hatk and vecc =-hati +7hatj -5hatk . Then OABC is tetrahedron. Statement 2 : Let A(veca) , B(vecb) and C(vecc) be three points such that vectors veca, vecb and vecc are non-coplanar. Then OABC is a tetrahedron, where O is the origin.

A point moves with uniform acceleration and v_(1), v_(2) , and v_(3) denote the average velocities in the three successive intervals of time t_(1).t_(2) , and t_(3) Which of the following Relations is correct?.