Question

${\huge{\underline{\small{\mathbb{\pink{DERIVATION \ OF \ PARALLELOGRAM \ LAW}}}}}}$​

Answer 1

Answer:

In Mathematics, the parallelogram law is the fundamental law that belongs to elementary Geometry. This law is also known as parallelogram identity. In this article, let us look at the definition of a parallelogram law, proof, and parallelogram law of vectors in detail.

Parallelogram Law of Addition

The Parallelogram law states that the sum of the squares of the length of the four sides of a parallelogram is equal to the sum of the squares of the length of the two diagonals. In Euclidean geometry, it is necessary that the parallelogram should have equal opposite sides.

Parallelogram Law

If ABCD is a parallelogram, then AB = DC and AD = BC. Then according to the definition of the parallelogram law, it is stated as

2(AB)2 + 2 (BC)2 = (AC)2 + (BD)2.

In case the parallelogram is a rectangle, then the law is stated as:

2(AB)2 + 2 (BC)2 = 2(AC)2

This is because in a rectangle, two diagonals are of equal lengths. i.e., (AC = BD)

Answer 2

Step-by-step explanation:

The parallelogram law of vector addition states that if two vectors are considered to be the two adjacent sides of a parallelogram with their tails meeting at the common point, then the diagonal of the parallelogram originating from the common point will be the resultant vector.

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