For two vectors `vec(A)` and `vec(B)` if `vec(A) + vec(B) = vec(C)` and `A +B = C`, then prove that `vec(A)` and `vec(B)` are parallel to each other.

If vec(A) +vec(B) = vec(C) and A^(2) +B^(2) = C^(2) , then prove that vec(A) and vec(B) are perpendicular to each other.

Three vector vec(A) , vec(B) , vec(C ) satisfy the relation vec(A)*vec(B)=0 and vec(A).vec(C )=0 . The vector vec(A) is parallel to

If |vec a+vec b|=|vec a-vec b|, show that the vectors vec a and vec b are perpendicular to each other.

For any two vectors vec a and vec b prove that | vec a + vec b | <= | vec a | + | vec b |

If vec(a), vec(b), vec(c ) are three vectors such that vec(a)xx vec(b)=vec(c ), vec(b)xx vec(c )=vec(a) , prove that vec(a), vec(b), vec(c ) are mutually at right angles and |vec(b)|=1, |vec(c )|=|vec(a)| .

Prove that for any two vectors vec(a) and vec(b), vec(a).(vec(a)xx vec(b))=0 . Is vec(b).(vec(a)xx vec(b))=0 ?

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

If vec a and vec b are two vectors such that |vec a+vec b|=|vec a|, then prove that vector 2vec a+vec b is perpendicular to vector vec b

Let vec(a).vec(b) and vec(c ) be three mutually perpendicular vectors each of unit magnitude. If vec(A) = vec(a) + vec(b) + vec(c ),  vec(B) = vec(a)- vec(b) + vec(c ) and vec(C ) = vec(a) - vec(b) - vec(c ) , then which one of the following is correct?

Let vec a,vec b,vec c are three non-zero vectors such that vec a xxvec b=vec c and vec b xxvec c=vec a; prove that vec a,vec b,vec c are mutually at righ angles such that |vec b|=1 and |vec c|=|vec a|