`vec a, vec b, vec c, vec d` are four distinct vectors satisfying the conditions `vec a xx vec b=vec c xx vec d and vec a xx vec c=vec b xx vec d,` then prove that `vec a. vec b+vec c. vec d!=vec a. vec c+ vec b. vec d.`

vec a, vec b, vec c, vec d are four distinct vectors satisfying the conditions vec a xxvec b = vec c xxvec d and vec a xxvec c = vec b xxvec d then prov that vec a * vec b + vec c.vec d! = vec a * vec c + vec b.vec d

If vec a xxvec b=vec c xxvec d and vec a xxvec c=vec b xxvec d then show that vec a-vec d is parallel to vec b-vec c where a!=d and b!=c

If vec a,vec b,vec c and vec d are distinct vectors such that vec a xxvec c=vec b xxvec d and vec a xxvec b=vec c xxvec d prove that (vec a-vec d)vec b-vec c!=0

Prove that [vec a,vec b,vec c+vec d]=[vec a,vec b,vec c]+[vec a,vec b,vec d]

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)

(vec a xxvec b) xx (vec c xxvec d) + (vec a xxvec c) xx (vec d xxvec b) + (vec a xxvec d) xx (vec b xxvec c)

36. If vec a, vec b, vec c and vec d are unit vectors such that (vec a xx vec b) .vec c xx vec d = 1 and vec a.vec c = 1/2 then a) vec a, vec b and vec c are non-coplanar b) vec b, vec c, vec d are non -coplanar c) vec b, vecd are non parallel d) vec a, vec d are parallel and vec b, vec c are parallel

vec a, vec b, vec c, dare any four vectors then (vec a xxvec b) xx (vec c xxvec d) is a vector Perpendicular to vec a, vec b, vec c, vec d

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