is equal in magnitude
to the volume of the parallelepiped formed on the three vectors,
Answer:
Volume of a parallelepiped. As shown in Fig. 7.98, consider
a parallelepiped having the three non-coplanar vectors 
and 
as edges meeting
at a point O. Let
and 
.
Fig. 7.98 Volume of a
parallelepiped.
Then, 
is a vector
perpendicular to the plane of 
and
. Let 
be the angle
between 
and . Clearly, 
is the height of
the parallelepiped orthogonal to it
its base.
Now,
a.
= Base area of the
parallelopiped
height
of the parallelepiped on this base
=
Volume of the parallelopiped having me vectors 
along edges meeting
at a point.
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