Prove that `vecixx(vecjxxveck)=vec0`

Prove that : vecixx(vecaxxveci)+vecjxx(vecaxxvecj)+veckxx(vecaxxveck)=vec(2a)

Prove that vecaxx(vecbxxvecc)+vecbxx(veccxxveca)+veccxx(vecaxxvecb)=vec0

If veca= vecP + vecq, vecP xx vecb = vec0 and vecq. Vecb =0 then prove that (vecbxx(veca xx vecb))/(vecb.vecb)=vecq

If veca= vecP + vecq, vecP xx vecb = vec0 and vecq. vecb =0 then prove that (vecbxx(veca xx vecb))/(vecb.vecb)=vecq

If veca,vecb,vecc and vecas\', vecb\', vecc\' are reciprocal system of vectors prove that vecaxxvecb+vecbxxvecb+veccxxvecc\'=vec0

Prove that GvecA+GvecB+GvecC=vec0 , if G is the centroid of Delta ABC.

Prove that vec(a)xx(vec(b)+vec(c))+vec(b)xx(vec(c)+vec(a))+vec(c)xx(vec(a)+vec(b))=0

If vec a=vec p+vec q,vec p xxvec b=0 and vec q*vec b=0 then prove that (vec b xx(vec a xxvec b))/(vec b*vec b)=vec q

If vec a,vec b,vec c be the vectors represented by theside sof a triangle,taken in order,then prove that vec a+vec b+vec c=vec 0

If a, b and c are any three vectors, then prove that vec a.(vec b+vec c)=(vec a.vec b)+(vec a.vec c)