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Properties of Diagonal of a Parallelogram

ABCD is a par...

Question

$A B C D$ is a parallelogram with $- - \to A C$ and $- - \to B D$ as diagonals. Then $- - \to A C - - - \to B D =$

4 - - \to A B

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3 - - \to A B

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2 - - \to A B

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- - \to A B

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Solution

The correct option is C $2 - - \to A B$
In $Δ A B C$
$\to a + \to b = - - \to A C$
In $Δ A B D$
$\to a + - - \to B D = \to b$ or $- - \to B D = \to b - \to a$
$- - \to A C - - - \to B D = \to a + \to b - (\to b - \to a)$
$= 2 \to a = 2 - - \to A B$

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