Answer
(a) See the attached figure for geometric interpretation.
(b) $|a+b|^2+|a-b|^2=2|a|^2+2|b|^2$
Work Step by Step
(a) The sum of square of the two diagonals of a parallelogram equals to the sum of square of the four sides. See the attached figure for geometric interpretation.
(b) $|a+b|^2+|a-b|^2=(a+b) \cdot (a+b)+(a-b) \cdot (a-b)$
$=a \cdot a+2a.b+b.b+a.a-2 a.b+b.b$
$=2 a.a+2b.b$
$=2|a|^2+2|b|^2$
Hence, $|a+b|^2+|a-b|^2=2|a|^2+2|b|^2$
