1
Question
ABCDEF is a regular hexagon . The centre of hexagon is a point O. Then the value of
−−→AB+−−→AC+−−→AD+−−→AE+−−→AF is
−−→AB+−−→AC+−−→AD+−−→AE+−−→AF is
Open in App
Solution
The correct option is D 6−−→AO
We have
−−→AB+−−→AC+−−→AD+−−→AE+−−→AF
We have
−−→AB+−−→AC=−−→AB+(−−→AB+−−→BC)=2−−→AB+−−→BC.............(i)
and
−−→AE+−−→AF=(−−→AD+−−→DE)+(−−→AD+−−→DE+−−→EF)=2−−→AD+2−−→DE+−−→DF............(ii)
From i and ii we see that −−→AB and −−→AC are vectorially opposite to −−→DE and −−→DF
Thus we get
−−→AB+−−→AC+−−→AD+−−→AE+−−→AF=3−−→AD=6−−→AO
We have
−−→AB+−−→AC+−−→AD+−−→AE+−−→AF
We have
−−→AB+−−→AC=−−→AB+(−−→AB+−−→BC)=2−−→AB+−−→BC.............(i)
and
−−→AE+−−→AF=(−−→AD+−−→DE)+(−−→AD+−−→DE+−−→EF)=2−−→AD+2−−→DE+−−→DF............(ii)
From i and ii we see that −−→AB and −−→AC are vectorially opposite to −−→DE and −−→DF
Thus we get
−−→AB+−−→AC+−−→AD+−−→AE+−−→AF=3−−→AD=6−−→AO
Suggest Corrections
0
Similar questions