Question

Prove by vector method that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

Answer 1

Given:- Parallelogram OABC

To Prove:-

AC² + OB² = OA² + AB² + BC² + CO²

Proof:- Let, O at origin

\(\vec a,\,\vec b\) and  \(\vec c\) be position vector of A, B and C respectively

Therefore,

the vectors form sides of triangle

Take RHS

OA² + AB² + BC² + CO²

Thus from equation (iii) and (iv),

we get

LHS = RHS

Hence proved