Vectors `vecm, vecn, vecr` are such that `vecm + vecn = vecr = 0` prove that `vecm xx vecn = vecn xx vecr = vecr xx vecm`.

If vecp xx vecq = vecm xx vec n and vecp xx vec m = vecq xx vecn , show that vecp- vecn is parallel to vecq - vecm where vecp ne vecn and vecq ne vecm .

If vecl,vecm,vecn are three non coplanar vectors prove that [vecl vecm vecn](vecaxxvecb) =|(vec1.veca, vec1.vecb, vec1),(vecm.veca, vecm.vecb, vecm),(vecn.veca, vecn.vecb, vecn)|

If vecl,vecm,vecn are three non coplanar vectors prove that [vec vecm vecn](vecaxxvecb) =|(vec1.veca, vec1.vecb, vec1),(vecm.veca, vecm.vecb, vecm),(vecn.veca, vecn.vecb, vecn)|

If vecl,vecm,vecn are three non coplanar vectors prove that [vecl vecm vecn](vecaxxvecb) =|(vec1.veca, vec1.vecb, vec1),(vecm.veca, vecm.vecb, vecm),(vecn.veca, vecn.vecb, vecn)|

vecu and vecn are unit vectors and t is a scalar. If vecn.veca!=0 solve the equation vecrxxveca=vecu , vecr.vecn=t

vecu and vecn are unit vectors and t is a scalar. If vecn.veca!=0 solve the equation vecrxxveca=vecu , vecr.vecn=t

Solve the vector equation vecr xx vecb = veca xx vecb, vecr.vecc = 0 provided that vecc is not perpendicular to vecb

Solve the vector equation vecr xx vecb = veca xx vecb, vecr.vecc = 0 provided that vecc is not perpendicular to vecb

If veca and vecb are othogonal unit vectors, then for a vector vecr non - coplanar with veca and vecb vector vecr xx veca is equal to