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

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

If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ,a n d vec c are nonzero vectors, then 1. vec a , vec b ,a n d vec c can be coplanar 2. vec a , vec b ,a n d vec c must be coplanar 3. vec a , vec b ,a n d vec c cannot be coplanar 4.none of these

36. If vec a, vec b,vec c and vec d are unit vectors such that (vec a xx vec b) . vec c xx vec d= 1 and vec a.vec c =1/2 then a) vec a, vec b and vec c are non-coplanar b) vec b, vec c ,vec d are non -coplanar c) vec b, vecd are non parallel d) vec a , vec d are parallel and vec b, vec c are parallel

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