If `vec A, vec B and vec C` are vectors such that `|vec B|-|vec C|`. Prove that `[(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0`

If vec A, vec B and vec C are vectors such that | vec B | - | vec C | * Prove [(vec A + vec B) xx (vec A + vec C)] xx (vec B + vec C) * (case B + case C) = 0

If vec a, vec b, vec c are three vectors such that | vec b | = | vec c | then {(vec a + vec b) xx (vec a + vec c)} xx {(vec b xxvec c)} * (vec b + vec c) =

Prove that (vec a-vec b)(vec b-vec c)xx(vec c-vec a)=0

If three vectors vec A, vec B and vec C are such that vec A .vec B =vec A .vec C , vec A xx vec B = vec A xx vec C , vec A!= vec 0 then prove that vec B =vec C .

If vec a, vec b and vec c are non coplaner vectors such that vec b xxvec c = vec a, vec c xxvec a = vec b and vec a xxvec b = vec c then | vec a + vec b + vec c | =

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

(vec a-vec b)*{(vec b-vec c)xx(vec c-vec a)}=0

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)

If vec a ,\ vec b ,\ vec c are three vectors such that vec adot\ vec b= vec adot\ vec c and vec a\ xx\ vec b= vec a\ xx\ vec c ,\ vec a\ !=0 , then show that vec b= vec c .

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