Prove that `vec i xx(vecjxxveck)=vec0`

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

Let the pairs a , b,and c ,d each determine a plane. Then the planes are parallel if a. ( vec axx vec c)xx( vec bxx vec d)= vec0 b. ( vec axx vec c).( vec bxx vec d)= vec0 c. ( vec axx vec b)xx( vec cxx vec d)= vec0 d. ( vec axx vec b).( vec cxx vec d)= vec0

Given vec(A)xxvec(B)=vec(0) and vec(B)xxvec(C )=vec(0) Prove that vec(A)xxvec(C )=vec(0)

If vec a ,\ vec b ,\ vec c be the vectors represented by the sides of a triangle, taken in order, then prove that vec a+ vec b+ vec c= vec0dot

If vec a= vec p+ vec q , vec pxx vec b=0a n d vec qdot vec b=0, then prove that ( vec bxx( vec axx vec b))/( vec bdot vec b)= vec qdot

If vec a+vec b+vec c=0 , prove that (vec a xx vec b)=(vec b xx vec c)=(vec c xx vec a)

Prove that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b) and interpret it geometrically.

If axx(bxxc)=(axxb)xxc , then ( vec cxx vec a)xx vec b= vec0 b. vec cxx( vec axx vec b)= vec0 c. vec bxx( vec cxx vec a) =0 d. ( vec cxx vec a)xx vec b= vec bxx( vec cxx vec a)= vec0

For any three vectors a b,c, show that vec a xx (vec b +vec c)+vec b xx (vec c +vec a) +vec cxx(vec a + vec b)=0