Let ` vec O A= vec a , vec O B=10 vec a+2 vec b ,a n d vec O C=bw h e r eO` is origin. Let `p` denote the area of th quadrilateral `O A B Ca n dq` denote the area of teh parallelogram with `O Aa n dO C` as adjacent sides. Prove that `p=6qdot`

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

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.

A B C D is quadrilateral such that vec A B= vec b , vec A D= vec d , vec A C=m vec b+p vec ddot Show that he area of the quadrilateral A B C Di s1/2|m+p|| vec bxx vec d|dot

If vec P O+ vec O Q= vec Q O+ vec O R , show that the point, P ,Q ,R are collinear.

Let vec a , vec b , vec c , vec d be the position vectors of the four distinct points A , B , C , Ddot If vec b- vec a= vec c- vec a , then show that A B C D is parallelogram.

Let vec a , vec b , vec c , vec d be the position vectors of the four distinct points A , B , C , Ddot If vec b- vec a= vec a- vec d , then show that A B C D is parallelogram.

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