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

Given a×b = c and b×c = a. From a×b = c, c is perpendicular to both a and b. From b×c = a, a is perpendicular to both b and c. Therefore a, b, c are mutually perpendicular (orthogonal in pairs). Taking magnitudes: |c| = |a||b|sin(angle between a,b) = |a||b| (since they are perpendicular). Similarly |a| = |b||c|. From these, |a| = |b|²|a|, so |b| = 1. Then |c| = |a|, and from |a| = |b||c| = |c|, consistent. Also from a×b = c, |c| = |a||b| = |a|, so |a| = |a|, and we get |a| = |c|. Using the third relation derivable, all are unit vectors. Hence both statements are correct.