Question

P vector + q vector = Rvector and p vector - qvector =s vector,So Prove that r^2+s^2=2(p^2+q^2)

Answer 1

Explanation:

p + q = r

p + q = √p² + q² + 2pq.cos∅

⇒ r = √p² + q² + 2pq.cos∅

on squaring both the sides,

r² = p² + q² + 2pq.cos∅      (equation 1)

now, p - q = s

p - q = √p² + q² - 2pq.cos∅

⇒ s = √p² + q² - 2pq.cos∅

on squaring both the sides

s² = p² + q² - 2pq.cos∅     (equation 2)

on adding equation 1 & 2 we get,

r² + q² = (p² + q² + 2pq.cos∅) + (p² + q² - 2pq.cos∅)

⇒ r² + q² = 2p² + 2q²

⇒ r² + q² = 2(p² + q²)

hence proved

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