If `A=(0,1)B=(1,0),C=(1,2),D=(2,1)` , prove that ` vec A B= vec C Ddot`

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

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.

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 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

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 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

Given vec(A)xxvec(B)=vec(0) and vec(B)xxvec(C )=vec(0) Prove that vec(A)xxvec(C )=vec(0)

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

Statement 1: In DeltaA B C , vec (A B)+ vec (BC)+ vec (C A)=0 Statement 2: If vec (O A)= vec a , vec (O B)= vec b ,t h e n \ vec (A B)= vec a+ vec b

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 vec(a), vec(b) and vec(c) are three vectors such that vec(a) times vec(b)=vec(c) and vec(b) times vec(c)=vec(a)," prove that "vec(a), vec(b), vec(c) are mutually perpendicular and abs(vec(b))=1 and abs(vec(c))=abs(vec(a)) .

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