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Mathematics
Mathematics
Problem
A plane cutting the axes in
P
,
Q
,
R
P, Q, R
P
,
Q
,
R
passes through
(
α
−
β
,
β
−
γ
,
γ
−
α
)
(\alpha - \beta, \beta - \gamma, \gamma - \alpha)
(
α
−
β
,
β
−
γ
,
γ
−
α
)
. If
O
O
O
is the origin, then locus of centre of sphere
O
P
Q
R
OPQR
O
P
QR
is a.
α
x
+
β
y
+
γ
z
=
4
\alpha x + \beta y + \gamma z = 4
α
x
+
β
y
+
γ
z
=
4
b.
(
α
−
β
)
x
+
(
β
−
γ
)
y
+
(
γ
−
α
)
z
=
0
(\alpha - \beta)x + (\beta - \gamma)y + (\gamma - \alpha)z = 0
(
α
−
β
)
x
+
(
β
−
γ
)
y
+
(
γ
−
α
)
z
=
0
c.
(
α
−
β
)
y
z
+
(
β
−
γ
)
z
x
+
(
γ
−
α
)
x
y
=
2
x
y
z
(\alpha - \beta)yz + (\beta - \gamma)zx + (\gamma - \alpha)xy = 2xyz
(
α
−
β
)
y
z
+
(
β
−
γ
)
z
x
+
(
γ
−
α
)
x
y
=
2
x
y
z
d.
(
1
α
2
+
1
β
2
+
1
γ
2
)
(
x
2
+
y
2
+
z
2
)
=
x
y
z
\left(\frac{1}{\alpha^2} + \frac{1}{\beta^2} + \frac{1}{\gamma^2}\right)(x^2 + y^2 + z^2) = xyz
(
α
2
1
+
β
2
1
+
γ
2
1
)
(
x
2
+
y
2
+
z
2
)
=
x
y
z
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