If a,b,c are vectors such that a×b=c,b×c=a,c×a=b . Show that a,b,c are mutually perpendicular unit vectors.

Since a×b=c, a and b lie in the same plane. (Using properties of cross product). Also, a and b are perpendicular to c.....(1)Similarly, if b and c are considered in a single plane, they are perpendicular to a....(2)Likewise, when c and a are in a single plane, they are perpendicular to b....(3)From (1),(2),(3) a, b and c are all perpendicular to each other.