Let a × b = c and b × c = a. Consider the following statements: I. a, b, c are pairwise orthogonal. II. a, b, c are unit vectors. Which of the statements given above is/are correct?

Since a × b = c, vector c is perpendicular to both a and b. Since b × c = a, vector a is perpendicular to both b and c. This means a, b, c are pairwise orthogonal — statement I is correct. Taking magnitudes: |c| = |a||b|sin(π/2) = |a||b|, and |a| = |b||c|sin(π/2) = |b||c|. From first: |c| = |a||b|; substituting into second: |a| = |b|·|a||b| = |a||b|², so |b|² = 1, |b| = 1. Then |c| = |a|, and from a perpendicular to c and b × c = a with |b| = 1: |a| = |c|. Also c × a = b (from cyclic property of orthogonal triad), giving |b| = |c||a|, so |a||c| = 1, with |a| = |c|, so |a|² = 1, hence |a| = |c| = 1. All are unit vectors — statement II is correct.