Using vector method, prove that if the diagonals of a parallelogram are equal in length, then it is a rectangle.

Hello student,

Using Parallelogram law of vector addition you will find that the diagonals are a+b & a-b if a & b are the vectors which are the sides of the diagonal.
a-b=a+b
Then sq.root(a^2+b^2-2abcosθ)=sq.root(a^2+b^2... (Here θ is the angle between the two vectors)
Simplifing you will get 4abcosθ=0
Since a& b are magnitudes & can never be equal to zero.
Hence
cosθ must be equal to zero i.e. cosθ=0
which is possible only if θ=90 degrees.
Thus Angle between vectors is 90 degrees. So the parallelogram is a rectangle

Thanks and Regards

Shaik Aasif

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