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

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

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)| , then A, B, C form

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

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

Prove that the resultant of two forces acting at point O and represented by vec O B and vec O C is given by 2 vec O D ,where D is the midpoint of BC.

Prove that the resultant of two forces acting at point O and represented by vec O B and vec O C is given by 2 vec O D ,where D is the midpoint of BC.

If 2 vec A C = 3 vec C B , then prove that 2 vec O A =3 vec C B then prove that 2 vec O A + 3 vec O B =5 vec O C where O is the origin.

Statement 1: In DeltaA B C , vec (A B)+ vec (BC)+ vec (C A)=0 Statement 2: If vec (O A)= vec a , vec (O B)= vec b ,t h e n \ vec (A B)= vec a+ vec b

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.