Let (ai,j ) be a skew-symmetric matrix of order 3 × 3. Let vi , i = 1, 2, 3, be smooth functions of a parameter s satisfying the system of differential equations dvi ds = X 3 j=1 ai,jvj, for i = 1, 2, 3. Furthermore, assume that for some initial value s0, the vectors v1(s0), v2(s0) and v3(s0) are orthonormal. Show that for all values of s, the vectors v1(s), v2(s) and v3(s) are orthonormal.