Show that veca.(vecbxxvec c) is equal in magnitude to the volume of the parallelopiped formed on the three vectors, veca,vecb and vec c

Show that veca.(vecbxxvec c) is equal in magnitude to the volume of th

1.	Show that veca.(vecbxxvec c) is equal in magnitude to the volume of the parallelopiped formed on the three vectors, veca,vecb and vec c
Answer» Solution :Suppose `VEC(OA)=vecb,vec(OC)=vecc and vec(OE)=VECA` `vecb and vec c` are adjacent sides of parallelogram OABC Area of `squareOABC,vecS=vecbxxvecc` `:.Shatn=vecbxxvecc` where `HATN` unit vector perpendicular to plane form by `vecb and vecc and theta` is angle between `veca and vecS`. `:.veca.(vecbxxvecc)=veca.vecS [because vecbxxvecc=vecS]` `=aScostheta` `=(acostheta)S` `=hS""......(1)` where in `DeltaEOE., EE.=h=acostheta` Suppose VOLUME of parallelepiped OABCDEF is V. `:.V` = Area of `squareOABCxx` perpendicular (h) of parallelogram OABC from E `:. V=sh"".....(2)` From result (1) and (2) `veca.(vecbxxvecc)=V`