# Show that a.(b×c) is equal in magnitude to the volume of the parallelopiped formed on the three vectors, a, b and c.

#### A parallelopiped with origin O and sides a,b, and c is shown in the following figure.

Volume of parallelopiped=abc

Let ^n be a unit vector perpendicular to both →b and →c. Hence ^n and →c have the same direction.

Therefore, →b×→c=bcsinθ ^n=bc^n

→a.(→b×→c)=a.(bc^n)

=abc= Volume of parallelopiped