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I think you are asking for a system from this vector equation that you can then get Sage to solve. To create such a system, try:

ans1=V_ra+omega.cross_product(P)
sys=[ans1[i]==V_fa[i] for i in range(0,3)]

Then, you get the result:

[-L^2*psi_d^2 + V == V_f*cos(phi), 0 == V_f*sin(phi), 0 == 0]

Solving the first equation for psi_d can be done by:

solve(sys[0],psi_d)

and gives:

[psi_d == -sqrt(-V_f*cos(phi) + V)/L, psi_d == sqrt(-V_f*cos(phi) + V)/L]

Sage does not seem to like the idea of solving all three equations at once. You might be able to avoid this by specifying more information about phi.