`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`

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

ABCDE is a pentagon. Prove that the resultant of force vec A B , vec A E , vec B C , vec D C , vec E D and vec A C ,is 3 vec A C .

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

If A ,B ,C ,D be any four points in space, prove that | vec A Bxx vec C D+ vec B Cxx vec A D+ vec C Axx vec B D|=4 (Area of triangle ABC)

If A B C D E F is a regular hexagon, them vec A D+ vec E B+ vec F C equals 2 vec A B b. vec0 c. 3 vec A B d. 4 vec A B

A , B , C , D are any four points, prove that vec A Bdot vec C D+ vec B Cdot vec A D+ vec C Adot vec B D=4(Area \ of triangle ABC).

Prove that [ vec a , vec b , vec c+ vec d]=[ vec a , vec b , vec c]+[ vec a , vec b , vec d]

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

In a regular hexagon A B C D E F ,\ A vec B=a ,\ B vec C= vec b\ a n d\ vec C D=c Then\ vec A E= a. vec a+ vec b+ vec c b. 2 vec a+ vec b+ vec c c. vec b+ vec c d. vec a+2 vec b+2 vec c

If vec a , vec b , vec ca n d vec d are the position vectors of the vertices of a cyclic quadrilateral A B C D , prove that (| vec axx vec b+ vec bxx vec d+ vec d xx vec a|)/(( vec b- vec a)dot( vec d- vec a))+(| vec bxx vec c+ vec cxx vec d+ vec d xx vec b|)/(( vec b- vec c)dot( vec d- vec c))=0dot