In a regular hexagon $A B C D E F$ , $¯ ¯¯¯¯¯¯ ¯ A B + ¯ ¯¯¯¯¯¯ ¯ A C + ¯ ¯¯¯¯¯¯¯ ¯ A D + ¯ ¯¯¯¯¯¯ ¯ A E + ¯ ¯¯¯¯¯¯ ¯ A F = k ¯ ¯¯¯¯¯¯¯ ¯ A D$ , then $k$ is equal to

1

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3

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0

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Solution

The correct option is B $3$
$\to A B = \to A D + \to D C + \to C B$
$\to A C = \to A D + \to D C$
$\to A D = \to A D$
$\to A E = \to A D + \to E D \to D E$
$\to A F = \to A D + \to D E + \to E F$
On adding all
$\to A B + \to A C + \to A D + \to A E + \to A F = 5 \to A D + 2 (\to D C + \to D E) + (\to C B + \to E F)$
$= 5 \to A D + 2 (\to D O) + \to D A$
$= 5 \to A D + 2 (\to D A)$
$= 5 (\to A D) - 2 (\to A D)$
$= 3 \to A D$
Value of $k = 3$ .

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