ABCDE is a pentagon. Prove that
$- - \to A B + - - \to B C + - - \to C D + - - \to D E + - - \to E A = \to 0$ .

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Solution

( $\to A B + \to B C) + (\to C D + \to D E) + \to E A$
$= \to A C + (\to C E + \to E A)$
$= \to A C + \to C A$
Both are equal in magnitude but opposite in direction
thus , $\to A C + \to C A = 0$

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