How to determine Euler parameters?

Question

I have two questions and I can't solve the second one. Here it goes:

Question 1

Consider a normalized system of units where µ = 1, Earth radius = 6378.165 km is the length unity, and T = 806.81 s is the time unit. Since the position and velocity vector are given by r = 2.0i + 2.0j + 2.0k and v = -0.4i + 0.2j + 0.4k, respectively, determine the keplerian elements (a, e, i, Ω, ω, M) of the spacecraft orbit, and select the correct option.

My answers are:

• a=4.6;
• e=0.3;
• i=54deg;
• Omega=14.3deg;
• omega=355.4deg;
• M=26.3deg

So the next question (which I don't know what do to) is:

Question 2.

Considering the classical Keplerian elements found in Question 8, determine the Euler parameters.(Beta1, Beta2 and Beta3).

Please help me to understand this.