Non-zero vectors p and q satisfy ∣p∣=∣q∣=5 and p⋅q=0.
(i) Prove that (p+q)×(p−q)=50.
(ii) Hence find the area of the parallelogram whose adjacent sides are p+q and p−q.
(iii) Compare the area obtained in part (ii) with the sum of the areas of the squares having sides p and q, and interpret the result geometrically.