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

If vec P O+ vec O Q= vec Q O+ vec O R , show that the point, P ,Q ,R 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 (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 , 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

Let vec O A= vec a , vec O B=10 vec a+2 vec ba n d vec O C= vec b ,w h e r eO ,Aa n dC are non-collinear points. Let p denotes the areaof quadrilateral O A C B , and let q denote the area of parallelogram with O Aa n dO C as adjacent sides. If p=k q , then find kdot

Let vec O A= vec a , hat O B=10 vec a+2 vec ba n d vec O C= vec b ,w h e r eO ,Aa n dC are non-collinear points. Let p denotes the areaof quadrilateral O A C B , and let q denote the area of parallelogram with O Aa n dO C as adjacent sides. If p=k q , then find kdot

A B C D is a quadrilateral and E and the point intersection of the lines joining the middle points of opposite side. Show that the resultant of vec O A , vec O B , vec O Ca n d vec O D is equal to 4 vec O E , where O is any point.

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.

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.