Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
A variable plane makes intercepts on
X
,
Y
X, Y
X
,
Y
and
Z
Z
Z
-axes and it makes a tetrahedron of volume 64 cu. u. The locus of foot of perpendicular from origin on this plane is a.
(
x
2
+
y
2
+
z
2
)
3
=
384
x
y
z
(x^2 + y^2 + z^2)^3 = 384 xyz
(
x
2
+
y
2
+
z
2
)
3
=
384
x
y
z
b.
x
y
z
=
681
xyz = 681
x
y
z
=
681
c.
(
x
+
y
+
z
)
(
1
x
+
1
y
+
1
z
)
2
=
16
(x + y + z) \left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right)^2 = 16
(
x
+
y
+
z
)
(
x
1
+
y
1
+
z
1
)
2
=
16
d.
x
y
z
(
x
+
y
+
z
)
=
81
xyz(x + y + z) = 81
x
y
z
(
x
+
y
+
z
)
=
81
Browse the problem library