# In a regular hexagon ABCDEF, if $\overrightarrow{AB}.$=$\vec{a}$ and vector BC = vector b,then express vector CD, vectorDE, vectorEF, vectorFA, vectorAC, vectorAD, vectorAF, vectorCF IN TERMS OF $\vec{a}$ AND VEC B ?

148 Points
13 years ago

Dear Aby Alex

given AB =a

BC =b      here a and b are vector

EF=-b

DE=-a

=2b

2b =a+b+CD

CD =b-a

and FA=-CD

=a-b

Ac=AB+BC

=a+b

AF=CD=b-a

and CF=2DE

=-2a

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Aby Alex
33 Points
13 years ago

Thank u very much

2 years ago
Dear student,
Please find the solution to the problem.

Given,
AB = a
BC = b      here a and b are vector
EF = – b
DE = – a
and we know thar AD = 2BC
=2b
2b = a+b+CD
CD = b – a
and FA = – CD
= a – b
AC = AB+BC
= a+b
AF = CD
= b – a
and CF = 2DE
= – 2a

Thanks and regards,
Kushagra