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Polygons(n>3)

Consider the ...

Question

Consider the regular hexagon $A B C D E F$ with centre at $O$ (origin).
Find resultant vector for $\to A D + \to E B + \to F C$

2 \to A B

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3 \to A B

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4 \to A B

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None of these

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Solution

The correct option is C $4 \to A B$
Consider the regular hexagon $A B C D E F$ with centre at $O$ (origin).
$\to A D + \to E B + \to F C = 2 \to A O + 2 \to O B + 2 \to O C$
$\to A D + \to E B + \to F C = 2 (\to A O + \to O B) + 2 \to O C$
$\to A D + \to E B + \to F C = 2 \to A B + 2 \to A B$
$(∵ \to O C = \to A B)$
$\to A D + \to E B + \to F C = 4 \to A B$

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