Let `A B C D` be a p[arallelogram whose diagonals intersect at `P` and let `O` be the origin. Then prove that ` vec O A+ vec O B+ vec O C+ vec O D=4 vec O Pdot`

If A B C D is a rhombus whose diagonals cut at the origin O , then proved that vec O A+ vec O B+ vec O C+ vec O D+ vec Odot

If A B C D is a rhombus whose diagonals cut at the origin O , then proved that vec O A+ vec O B+ vec O C+ vec O D+ vec Odot

Let vec a , vec b ,a n d vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a]=[ vec a vec b vec c]^2dot

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.

A B C D is a quadrilateral. E is the point of intersection of the line joining the midpoints of the opposite sides. If O is any point and vec O A+ vec O B+ vec O C+ vec O D=x vec O E ,t h e nx is equal to a. 3 b. 9 c. 7 d. 4

A , B , C , D are any four points, prove that vec A B dot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=0.

For any three vectors veca, vec b, vec c prove that (vec a + vec b)+ vec c = vec a + (vec b + vec c)

If vec a , vec b , vec c ,a n d vec d are four non-coplanar unit vector such that vec d make equal angles with all the three vectors vec a , vec ba n d vec c , then prove that [ vec d vec a vec b]=[ vec d vec c vec b]=[ vec d vec c vec a]dot

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

Let O A C B be a parallelogram with O at the origin and O C a diagonal. Let D be the midpoint of O Adot using vector methods prove that B Da n dC O intersect in the same ratio. Determine this ratio.