If $\to a a n d \to b$ are the vectors $- - \to A B a n d - - \to B C$ determined by the adjacent sides of a regular hexagon. What are the vectors determined by the other sides taken in order?

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Solution

Given:
$- - \to A B = \to a - - \to B C = \to b$
EF is parallel to BC and equal to its length
hence ,
$- - \to F E = \to b$
and ED vector is also eqaul to AB
$- - \to E D = \to a$

let the center point is O
then $- - \to B O = - - \to B C + - - \to C O = \to b - \to a$
now $- - \to A F$ is parallel to $- - \to B O$
hence , $- - \to A F = \to b - \to a$
And $- - \to C D$ vector is also equal to $- - \to B O$
Hence, $- - \to C D = \to b - \to a$

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