Show that `overset rarr(a). (overset rarr(b) xx overset rarr(c ))` is equal in magnitude to the volume of the parallelopiped formed on the three vectiors, `overset rarr(a), overset rarr(b) and overset rarr(c )`.

Explanation

Let a parallelopiped be formed on the three vectors
`overset rarr(OA) = overset rarr(a), overset rarr(OB) = overset rarr(b)` and `overset rarr(OC) = overset rarr(c )`, Fig.
Now, `overset rarr(b) xx overset rarr(c ) = bc sin 90^(@) hatn = bc hatn`
when `hat n` is unit vector along `overset rarr(OA)` perpendicular to the plane contaning `overset rarr(b)` and `overset rarr(c )`.
Now, `overset rarr(a). (overset rarr(b) xx overset rarr(c )) = overset rarr(a). bc hatn = (a) (bc) cos 0^(@) = abc`
which is equal in magnitude to the volume of the parallelopiped.