Question 1. Let (a;j) be a skew-symmetric matrix of order 3 x 3. Let vi, i = 1,2, 3, be smooth functions of a parameter s satisfying the system of differential equations %3D dv; Lai,jVj, for i = 1, 2, 3. %3| ds j=1 Furthermore, assume that for some initial value so, the vectors v1(so),v2(so) and v3(s0) are orthonormal. Show that for all values of s, the vectors vi(s), v2(s) and v3(s) are orthonormal.

Q: I need help for problem 6. Thanks!

A: Part(A)Given: -

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.