If 2` vec A C` = 3` vec C B` , then prove that 2` vec O A` =3` vec C B` then prove that 2` vec O A` + 3` vec O B` =5` vec O C` where `O` is the origin.

If vec a + vec b + vec c = o, prove that vec a xxvec b = vec b xxvec c = vec c xxvec a

If vec a,vec b,vec c are three vectors such that vec a+vec b+vec c=vec 0, then prove that vec a xxvec b=vec b xxvec c=vec c xxvec a

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)

Statement 1:Let A( vec a),B( vec b)a n dC( vec c) be three points such that vec a=2 hat i+ hat k , vec b=3 hat i- hat j+3 hat ka n d vec c=- hat i+7 hat j-5 hat kdot Then O A B C is a tetrahedron. Statement 2: Let A( vec a),B( vec b)a n dC( vec c) be three points such that vectors vec a , vec ba n d vec c are non-coplanar. Then O A B C is a tetrahedron where O is the origin.

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

If 2vec a + 3vec b + vec c = vec 0, then vec a xxvec b + vec b xxvec c + vec c xxvec a = 3vec b xxvec c

If a, b and c are any three vectors, then prove that vec a.(vec b+vec c)=(vec a.vec b)+(vec a.vec c)

If vec a,vec b and vec c are three non-zero vectors,prove that [vec a+vec b,vec b+vec c,vec c+vec a]=2[vec a,vec b,vec c]

vec a * {(vec b + vec c) xx (vec a + 2vec b + 3vec c)} = [vec with bvec c]

If | vec a | = | vec b | = 1, | vec c | = 3vec b * vec c = - (3) / (4) and vec a xxvec c = 2 (vec a xxvec b)