For any three vectors `veca,vecb,vec(c)` prove that `[vecbxxvec(c)" "vec(c)xxveca" "vecaxxvecb]=[vec(a)" "vecb" "vec(c)]^(2)`

If veca+vecb+vec(c)=vec0 , then prove that vecaxxvecb=vecbxxvec(c)=vec(c)xxveca .

If three vectors vec(a), vec(b), vec(c ) are such that vec(a) ne vec(0) and vec(a) xx vec(b)=2 (vec(a) xx vec(c )), |vec(a)| = |vec(c )| =1, |vec(b)|=4 and the angle between vec(b) and vec(c ) is cos^(-1) ((1)/(4)) , then vec(b)-2vec(c )= lamda vec(a) where lamda =

Show that [(vec(a)xxvec(b))xx(vec(a)xxvec(c)))].vec(d)=(veca.vecd)[vecavecbvec(c)] .

If vec(a)-vec(i)-2vec(j)-3vec(k), vec(b)=2vec(i)+vec(j)-vec(k) and vec(c )=vec(i)+3vec(j)-2vec(k) , verify that vec(a) xx (vec(b) xx vec(c )) = (vec(a).vec(c ))vec(b)-(vec(a).vec(b))vec(c ) .