Question: if the diagonals of a parallelogram are equal then show that it is a rectangle by vector method?
Answer: Yes if diagonals of a parallelogram are equal then it is a rectangle. Let PQRS be a parallelogram. To show that PQRS is a rectangle, we have to prove that one of its interior angles is 90º. Since PQRS is a parallelogram and one of its interior angles is 90º, PQRS is a rectangle.