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
Create a free account to view solution
View Solution FreeMore Introduction to 3D Questions
If O is the origin and A is the point (a, b, c) then the equation of the plane through A and at right angles to OA is -...The points A(5, -1, 1), B(7, -4, 7), C(1, -6, 10) and D(-1, -3, 4) are the vertices of a -...At 25oC molar conductance of 0.1 molar aqueous solution of ammonium hydroxide is 9.54 ohm-1 cm2mol-1 and at infinite dil...P ≡ (x1, y1, z1) and Q ≡ (x2, y2, z2 ) are two points if direction cosines of a line are l, m, n then projec...The equation of the plane passing through the lines and is -...