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Mathematics
Mathematics
Problem
Find the value of
λ
\lambda
λ
for which the plane
x
+
y
+
z
=
3
λ
x + y + z = \sqrt{3}\lambda
x
+
y
+
z
=
3
λ
touches the sphere
x
2
+
y
2
+
z
2
−
2
x
−
2
y
−
2
z
=
6
x^2 + y^2 + z^2 - 2x - 2y - 2z = 6
x
2
+
y
2
+
z
2
−
2
x
−
2
y
−
2
z
=
6
.
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