Using dot product of vectors, prove that a parallelogram, whose diagonals are equal, is a rectangle

Explanation

Take A B C D be a parallelogram


To prove A B C D be a rectangle provided the diagonals are equal.



`vec{{AC}}=vec{{AB}}+vec{{BC}} `


`vec{{BD}}=vec{{BC}}+vec{{CD}}=vec{{BC}}-vec{{AB}}`



But `(vec{{AC}})^{2}=(vec{{BD}})^{2}`



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