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Putnam
1959 Putnam
B5
B5
Part of
1959 Putnam
Problems
(1)
Putnam 1959 B5
Source: Putnam 1959
6/16/2022
Find the equation of the smallest sphere which is tangent to both of the lines
(
x
y
z
)
=
(
t
+
1
2
t
+
4
−
3
t
+
5
)
,
(
x
y
z
)
=
(
4
t
−
12
−
t
+
8
t
+
17
)
.
\begin{pmatrix} x\\y\\z \end{pmatrix} =\begin{pmatrix} t+1\\ 2t+4\\ -3t +5 \end{pmatrix},\;\;\;\begin{pmatrix} x\\y\\z \end{pmatrix} =\begin{pmatrix} 4t-12\\ -t+8\\ t+17 \end{pmatrix}.
x
y
z
=
t
+
1
2
t
+
4
−
3
t
+
5
,
x
y
z
=
4
t
−
12
−
t
+
8
t
+
17
.
Putnam
geometry
3D geometry
sphere
distance