Choose the correct option based on the parallelogram $A B C D$ .

- - \to A B

- - \to A D

- - \to D C

- - \to C B

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- - \to A B

= (

- - \to A D

- - \to D C

) +

- - \to C B

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- - \to A B

- - \to A D

+ (

- - \to D C

- - \to C B

)

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All of the above

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Solution

The correct option is D $All of the above$
From the associative law of vector addition
$- - \to A D$ + ( $- - \to D C$ + $- - \to C B$ ) = ( $- - \to A D$ + $- - \to D C$ ) + $- - \to C B$
and since, from triangle law of vector addition
$- - \to A B$ = $- - \to A D$ + $- - \to D B$ = $- - \to A D$ + ( $- - \to D C$ + $- - \to C B$ )

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