Let p and q be unit vectors. What is the maximum possible value of the expression ||p + q|² - |p - q|²| / (|p + q|² + |p - q|²)?

Correct answer: 1

Solution

Setting |p|=|q|=1, the numerator becomes |4(p*q)| and the denominator is 4, giving |p*q| = |cos(theta)| <= 1. The maximum value 1 is achieved when theta = 0 or pi.

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