Introduction to 3DHard
Question
A variable plane forms a tetrahedron of constant volume 64K3 with the coordinate planes and the origin, then locus of the centroid of the tetrahedron is -
Options
A.x3 + y3 + z3 = 6K2
B.xyz = 6k3
C.x2 + y2 + z2 = 4K2
D.x-2 + y-2 + z-2 = 4k-2
Solution
Let the tetrahedron cut x-axis, y-axis and z-axis at a, b & c respectively.
volume =
(Given)
Then 1/6 (abc) = 64k3 .... (1)
Let centroid be (x1, y1, z1)
∴ x1 =
, y1 = 
, z1 = 
put in (1) wet get
x1y1z1 = 6K3
The required locus is xyz = 6K3
volume =
(Given)Then 1/6 (abc) = 64k3 .... (1)
Let centroid be (x1, y1, z1)
∴ x1 =
, y1 = , z1 = put in (1) wet get
x1y1z1 = 6K3
The required locus is xyz = 6K3
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