Question

By using vector method prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the square of its sides.

Answer 1

\[\left|B-A\right|^2+\left|A+B\right|^2=(B-A)\cdot (B-A)+(A+B) \cdot (A+B)\\=B\cdot B - 2 A\cdot B+A\cdot A + A\cdot A + 2 A\cdot B + B\cdot B\\=\left|A\right|^2+\left|B\right|^2+\left|A\right|^2+\left|B\right|^2\]

Answer 2

thank u