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Vector Addition

ABCD is a par...

Question

$A B C D$ is a parallelogram and $A C, B D$ be its diagonals Then $\to A C + \to B D$ is

2 \to A B

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2 \to B C

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3 \to A B

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3 \to B C

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Solution

The correct option is A $2 \to B C$
$A B C D$ is a parallelogram so, $A B | | C D$ and $A D | | B C$
$\to A C = \to A B + \to B C$ (addition Theorem)
$\to B D = \to B A + \to A D$ (addition Theorem)
$\to A C + \to B D = \to A B + \to B C + \to B A + \to A D$
$= \to A B + \to B C - \to A B + \to B C$
$= 2 \to B C$

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