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

- - \to A C = - - \to A B + - - \to B C \neq - - \to A D + - - \to D C

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- - \to A C \neq - - \to A B + - - \to B C \neq - - \to A D + - - \to D C

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- - \to A C \neq - - \to A B + - - \to B C = - - \to A D + - - \to D C

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- - \to A C = - - \to A B + - - \to B C = - - \to A D + - - \to D C

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Solution

The correct option is D $- - \to A C = - - \to A B + - - \to B C = - - \to A D + - - \to D C$
In a parallelogram $- - \to A B = - - \to D C = \to a$ (say)
and $- - \to B C = - - \to A D = \to b$
According to the commutative law of vector addition
$\to a + \to b = \to b + \to a$

Hence,
$- - \to A B + - - \to B C = - - \to A D + - - \to D C$
and according to vector addition
$- - \to A B + - - \to B C = - - \to A C$

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