1) (10 pt) Show 6.6. =3 ij 2) (10 pt) Show jk . = aik 3)&4) Given [a]=(a;; ) =(e,e, ) as the direction cosine matrix. Recall that x =ajjx; where x=x e, = xe, is the same vector in the two coordinate systems. Show (10 pts each) 3 e = a e; 4) e, = ape (Hint: Pick x to be one of e, or e, in 3) and 4) and expresse, in terms of e, and vice versa) (*** Updated: Another hint: if f = ae, , what is a, in terms of F and e, ? **#) 5) (10pt) Let AXB =C, it is known that C =ce = Exabjex. Prove (or disprove) that c = &,ab for the ith component that goes with e; 6) (10pt) Let BX A= D, it is known that D = die, = & bajex. Prove (or disprove) that d = -c =-6, ab, for the kth component that goes with e