A particle P travels along an elliptical spiral path such that its position vector r is defined by r = (a cos bt i + c sin dt j + et k). When t = t₁, determine the coordinate direction angles α, β, and γ, which the binormal axis to the osculating plane makes with the x, y, and z axes. Solve for the velocity vp and acceleration ap of the particle in terms of their i, j, k components. The binormal is parallel to v_p × a_p. Why? Given:

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a = 2 m -1 b = 0.1 s 1 c = 1.5 m d = 0.1 s e = 2 m S t1 = 8 s