MathDB

We consider three vectors drawn from the same initial point

O,

of lengths

a,b

and

c

, respectively. Let

E

be the parallelepiped with vertex

O

of which the given vectors are the edges and

H

the parallelepiped with vertex

O

of which the given vectors are the altitudes. Show that the product of the volumes of

E

and

H

equals

(abc)^{2}

and generalize this result to

n

dimensions.

Problem Statement