for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) =

For any three vectors veca, vecb, vecc the value of [(veca-vecb, vecb-vecc, vecc-veca)] , is

For any three vectors veca, vecb, vecc the value of [(veca+vecb,vecb+vecc,vecc+veca)] is

for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) = 2 veca.vecb xx vecc .

If the vectors veca, vecb, and vecc are coplanar show that |(veca,vecb,vecc),(veca.veca, veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc)|=0

Three vectors veca,vecb,vecc are such that veca xx vecb=4(veca xx vecc) and |veca|=|vecb|=1 and |vecc|=1/4 . If the angle between vecb and vecc is pi/3 then vecb is

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 veca.vecb\'=veca.veca\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . The value of (vecaxxveca\')+(vecbxxvecb\')+(veccxxvecc\') is (A) veca+vecb+vecc (B) veca\'+vecb\'+vecc\' (C) 0 (D) none of these

Show that the vectors 2veca-vecb+3vecc, veca+vecb-2vecc and veca+vecb-3vecc are non-coplanar vectors (where veca, vecb, vecc are non-coplanar vectors).

i. If veca, vecb and vecc are non-coplanar vectors, prove that vectors 3veca-7vecb-4vecc, 3veca-2vecb+vecc and veca+vecb+2vecc are coplanar.

if veca + vecb + vecc=0 , then show that veca xx vecb = vecb xx vecc = vecc xx veca .