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

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

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

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

If vectors, vecb, vecc and vecd are not coplanar, the prove that vector (veca xx vecb) xx (vecc xx vecd) + ( veca xx vecc) xx (vecd xx vecb) + (veca xx vecd) xx (vecb xx vecc) is parallel to veca .

Prove that: (2veca-vecb)xx (veca+2vecb)=5vecaxxvecb .

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

The value of hati xx(hatixxa)+hatjxx(hatjxxa) +hatk xx(hatkxxa) is

Prove that (veca+3vecb)xx(veca+vecb)+(3veca-5vecb)xx(veca-vecb)=0

Prove that (veca.(vecbxxhati))hati+(veca.(vecbxxhatj))hatj+ (veca.(vecbxxhatk))hatk=vecaxxvecb

veca=2hati+hatj+2hatk, vecb=hati-hatj+hatk and non zero vector vecc are such that (veca xx vecb) xx vecc = veca xx (vecb xx vecc) . Then vector vecc may be given as