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Numerade Educator



Problem 63 Hard Difficulty

The Parallelogram Law states that
$$ {\mid a + b \mid}^2 + {\mid a - b \mid}^2 = 2 {\mid a \mid}^2 + 2 {\mid b \mid}^2 $$
(a) Give a geometric interpretation of the Parallelogram Law.
(b) Prove the Parallelogram Law. (See the hint in Exercise 62.)


a) The sum of the square of the length of the diagonals of a parallelogram, are equal to the square of the length of the four sides of the parallelogram.
b) $|\mathbf{a}+\mathbf{b}|^{2}+|\mathbf{a}-\mathbf{b}|^{2}=(\mathbf{a}+\mathbf{b}) \cdot(\mathbf{a}+\mathbf{b})+(\mathbf{a}+\mathbf{b}) \cdot(\mathbf{a}+\mathbf{b})$
$=2(\mathbf{a} \cdot \mathbf{a})+2(\mathbf{b} \cdot \mathbf{b})$
$=L . H . S$
$=R . H . S \quad$ (R.T.P)


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Video Transcript

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