If `A B C D` is quadrilateral and `Ea n dF` are the mid-points of `A Ca n dB D` respectively, prove that ` vec A B+ vec A D` +` vec C B` +` vec C D` =4 ` vec E Fdot`

If A B C D is quadrilateral and E and F are the mid-points of AC and BD respectively, prove that vec A B+ vec A D + vec C B + vec C D =4 vec E Fdot

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

A B C D is a parallelogram. If La n dM are the mid-points of B Ca n dD C respectively, then express vec A La n d vec A M in terms of vec A Ba n d vec A D . Also, prove that vec A L+ vec A M=3/2 vec A Cdot

A B C D is a parallelogram. If L and M are the mid-points of B C and D C respectively, then express vec A L and vec A M in terms of vec A B and vec A D . Also, prove that vec A L+ vec A M=3/2 vec A Cdot

A B C D E is pentagon, prove that vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

If D is the mid-point of the side B C of a triangle A B C , prove that vec A B+ vec A C=2 vec A Ddot

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .