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

Prove that In a parallelogram, opposite side are equal

Prove that : the parallelogram , inscirbed in a circle , is a rectangle.

If the two diagonals of a parallelogram are equal, it is a rectangle.

Prove that any cyclic parallelogram is a rectangle.

Prove that any cyclic parallelogram is a rectangle.

Using cross product of vectors, prove that sin(A+B)=sinAcosB+cosAsinBdot

Area of a parallelogram, whose diagonals are 3hati+hatj-2hatk and hati-3hatj+4hatk will be:

Using vectors, prove that the parallelogram on the same base and between the same parallels are equal in area.

Which of the following statements are true (T) and which are false (F)? (i) In a parallelogram, the diagonals are equal. (ii) In a parallelogram, the diagonals bisect each other. (iii) In a parallelogram, the diagonals intersect each other at right angles. (iv) In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram. (v) If all the angles of a quadrilateral are equal, it is a parallelogram. (vi) If three sides of a quadrilateral are equal , it is a parallelogram. (vii) If three angles of a quadrilateral are equal, it is a parallelogram. (viii) If all the sides of a quadrilateral are equal it is a parallelogram

What is dot product of two orthogonal vector ?