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Question

Assertion :If |a+b|=|ab|, then a and b are perpendicular to each other Reason: If the diagonals of a parallelogram are equal in magnitude, then the parallelogram is a rectangle.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Let a and b be two vectors
Hence
|a+b|=|ab|

a2+b2+2abcosθ=a2+b22abcosθ

Squaring on both the sides, we get
a2+b2+2abcosθ=a2+b22abcosθ
4abcosθ=0 ...(i)

If a0 b0
Then cosθ=0
θ=(2n1)π2 where nϵN

Hence a is perpendicular to b.
If a and b are adjacent sides of a parallelogram, then, the parallelogram is a rectangle. ...(from i).

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