Prove that `hatixx(vecaxxveci) + hatjxx(vecaxxvecj) + hatkxx(vecaxxveck)=2veca`

Prove that hati xx(vecaxxveci)+hatjxx(vecaxxvecj)+hatkxx(vecaxxveck)=2veca

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

For an vector veca the value of hatixx(vecaxxveci)+hatjxx(vecaxxhatj)+hatkxx(vecaxxveck) , is

If veca is any vector and hati,hatj and hatk are unit vectors along the x,y and z directions then hatixx(vecaxxhati)+hatjxx(vecaxxhatj)+hatkxx(vecaxxveck)= (A) veca (B) -veca (C) 2veca (D) 0

Prove that vecA.(vecAxxvecB)=0

For any vectors vecr the value of hatixx(vecrxxhati)+hatjxx(vecrxxhatj)+hatkxx(vecrxxhatk) , is

If hata=hati+2hatj+3hatk, hatb=hatixx(vecaxxhati)+hatjxx(vecaxxhatj)+hatkxx(vedaxxhatk) then length of vecb is equal to (A) sqrt(12) (B) 2sqrt(12) (C) 2sqrt(14) (D) 3sqrt(12)

Prove that (vecaxxvecb)^2=veca^2b^2-(veca.vecb)^2 .

Prove that: [(vecaxxvecb)xx(vecaxxvecc)].vecd=[veca vecb vecc](veca.vecd)

prove that (veca.hati)(vecaxxhati)+(veca.hatj)(vecaxxhatj)+(veca.hatk)(vecaxxhatk)=vec0