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Mathematics
Mathematics
Problem
A variable plane forms a tetrahedron of constant volume
64
K
3
64K^3
64
K
3
with the coordinate planes and the origin, then locus of the centroid of the tetrahedron is a.
x
3
+
y
3
+
z
3
=
6
k
3
x^3 + y^3 + z^3 = 6k^3
x
3
+
y
3
+
z
3
=
6
k
3
b.
x
y
z
=
6
k
3
xyz = 6k^3
x
y
z
=
6
k
3
c.
x
2
+
y
2
+
z
2
=
4
k
2
x^2 + y^2 + z^2 = 4k^2
x
2
+
y
2
+
z
2
=
4
k
2
d.
x
−
2
+
y
−
2
+
z
−
2
=
4
k
−
2
x^{-2} + y^{-2} + z^{-2} = 4k^{-2}
x
−
2
+
y
−
2
+
z
−
2
=
4
k
−
2
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