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Q.
Let $A B C D E F$ be a regular hexagon. If $A D=x B C$ and $C F=y A B$, then $x y=$
Vector Algebra
Solution:
Since $A B C D E F$ is a regular hexagon, from plane geometry, we have
$A D=2 B C$ and $F C=2 A B$
$\therefore A D=2 B C$ and $F C=2 A B\,\,\,\, (1)$.
Given that $A D=x B C$.
$\therefore 2 B C=x B C$, by (i)
$\Rightarrow x=2\,\,\,\,(2)$
Again, given that $C F=y A B$
or $-F C=y A B$.
$\therefore -2 A B=y A B$, using (ii)
$\Rightarrow y=-2\,\,\,\,(3)$.
From (ii) and (iii),
$x y=2(-2)=-4$.
