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Addition of Vectors

If A , B , C ...

Question

If A , B , C and D are any four points E and F are the middle points of AC and BD, respectively then prove that $\to C B + \to C D + \to A D + \to A B = 4 \to E F$

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Solution

$\to A B + \to A D + \to C B = 4 \to C F$
$A B + A D = 2 A F - - - - (1)$
$C B + C D = 2 C F - - - (2)$
$A B + A D + C B + C D = (A F + C F)$
$A B + A D + C B + C D = 2 (\to F A + \to C F)$
$A B + A D + C B + C D = - 2 (2 F C)$
$A B + A D + C B + C D = 4 E F$

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