If ` vec A O+ vec O B= vec B O+ vec O C` , prove that `A , B , C` are collinear points.

If vec AO+vec OB=vec BO+vec OC, prove that A,B,C are collinear points.

The position vectors of the points A,B,C are vec a, vec b, vec c respectively. If 3 vec a + 2 vec c= 5 vecb , are the points A,B,and C collinear? If so find AB:BC .

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

If vec a , vec b , vec c , vec d are the position vector of point A , B , C and D , respectively referred to the same origin O such that no three of these point are collinear and vec a + vec c = vec b + vec d , than prove that quadrilateral A B C D is a parallelogram.

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 are three non-zero vectors (no two of which are collinear), such that the pairs of vectors (vec a + vec b, vec c) and (vec b + vec c , vec a) are collinear, then vec a + vec b + vec c =

If vec a ,\ vec b ,\ vec c are three non-zero vectors, no two f thich are collinear and the vector vec a+ vec b is collinear with vec c ,\ vec b+ vec c is collinear with vec a ,\ t h e n\ vec a+ vec b+ vec c= a. vec a b. vec b c. vec c d. none of these

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that vec O Pdot vec O Q+ vec O Rdot vec O S= vec O Rdot vec O P+ vec O Qdot vec O S= vec O Q . vec O R+ vec O Pdot vec O S Then the triangle PQ has S as its: circumcentre (b) orthocentre (c) incentre (d) centroid

If vec a + vec b + vec c = o, prove that vec a xxvec b = vec b xxvec c = vec c xxvec a