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Putnam
1949 Putnam
A2
A2
Part of
1949 Putnam
Problems
(1)
Putnam 1949 A2
Source: Putnam 1949
3/20/2022
We consider three vectors drawn from the same initial point
O
,
O,
O
,
of lengths
a
,
b
a,b
a
,
b
and
c
c
c
, respectively. Let
E
E
E
be the parallelepiped with vertex
O
O
O
of which the given vectors are the edges and
H
H
H
the parallelepiped with vertex
O
O
O
of which the given vectors are the altitudes. Show that the product of the volumes of
E
E
E
and
H
H
H
equals
(
a
b
c
)
2
(abc)^{2}
(
ab
c
)
2
and generalize this result to
n
n
n
dimensions.
Putnam
vector
Volume