If `vec(AO)+vec(OB)=vec(BO)+vec(OC)`, show that the points A, B and C are collinear.

if vec (AO) + vec (O B) = vec (B O) + vec (O C) ,than prove that B is the midpoint of AC .

If vec(a), vec(b), vec(c) are three given vectors, show that the points having vectors 7vec(a)-vec(c), vec(a)+2vec(b) " and " -2vec(a)+3vec(b)+0.5vec(c) are collinear.

If vec(x), vec(y), vec(z) are three vectors, show that the points having positive vectors 7vec(x) - vec(z), vec(x) + 2vec(y) + 3vec(z) and -2vec(x) + 3vec(y) + 5vec(z) are collinear

For the vector vec(a) and vec (b) if |vec(a) + vec(b)| = |vec(a) - vec(b)| , show that vec(a) and vec (b) are perpendicular

If vec A O+ vec O B= vec B O+ vec O C , then A ,B and C are (where O is the origin) a. coplanar b. collinear c. non-collinear d. none of these

Three non-zero vectors vec(a), vec(b), vec(c) are such that no two of them are collinear. If the vector (vec(a)+vec(b)) is collinear with the vector vec(c) and the vector (vec(b)+vec(c)) is collinear with vector vec(a) , then prove that (vec(a)+vec(b)+vec(c)) is a null vector.

Let O be an interior points of triangleABC such that vec(OA)+2vec(OB)+3vec(OC)=vec0 , then the ratio of triangleABC to area of triangleAOC is

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 vec(b) - vec (c) , where to vec (a) != vec (d) and vec ( b) != vec (c )

If vec(a) + vec(b) + vec (c ) = vec(0) , show that vec(a) xx vec(b) = vec(b) xx vec(c ) = vec(c ) xx vec(a)

If vec(a),vec(b),vec (c ) are non - coplanar vectors vec (r) . vec(a) = vecr . vec(b) = vecr.vec(c ) = 0 , show that vec (r ) is a zero vector .