`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.`

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d)dot (vec b- vec c)!=0,

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,

If vec(a) xx vec(b)= vec(c ) xx vec(d), vec(a) xx vec(c )= vec(b) xx vec(d) , then

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\ xx\ vec b=\ vec c\ xx\ vec d\ and vec a\ xx\ vec c=\ vec b\ xx vec d show that vec a- vec d is parallel to vec b- vec c , where vec a!= vec d and vec b!= vec c

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)

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