Answer the following conceptual questions on the relationship among two vectors a and b:
(i) Explain why the condition a⋅b=0 is sufficient to conclude that non-zero vectors a and b are perpendicular, but does not convey any information when either vector is the zero vector.
(ii) Discuss whether the equation a×b=0 guarantees that the vectors are parallel when one of the vectors is the zero vector. Give reasons for your answer.
(iii) Provide one numerical example for each of the following cases and justify each claim:
(A) Two non-zero perpendicular vectors.
(B) Two non-zero parallel vectors.
(C) One zero vector and one non-zero vector satisfying a⋅b=0.
(D) One zero vector and one non-zero vector satisfying a×b=0.