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

Explanation

Let the adjacent sides of parallelogram be `vec a` and `vec b`
Then, Diagonal vectors will be `(vec a+ vec b)` and `(vec a-vec b)`
Sum of the squares of the diagonals
`=(vec a+ vec b)^2+(vec a- vec b)^2`
`=2(|vec a|^2+|vec b|^2)`
Sum of squares of sides
`=2(|vec a|^2+|vec b|^2)`
Hence the sum of the square
of the diagonals of a parallelogram is equal to the sum of the squares of its
sides.