The x, y, and z coordinates (in meters) of a particle P as a function of time (in seconds) are x 1⁄4 sin 3t, y 1⁄4 cos t, and z 1⁄4 sin 2t. At t 1⁄4 3s, determine:.(a) The velocity v, in Cartesian coordinates. (b) The speed v. (c) The unit tangent vector u (d) The angles θ θ)" and θ, tat v makes with the x-, y-, and z-axes. (e) The acceleration a in Cartesian coordinates. (f) The unit binormal vector u (g) The unit normal vector (h) The angles 9,, and that a makes with the x-, y-, and z-axes. (i) The tangential component at of the acceleration.(j) The normal component an of the acceleration. (k) The radius of curvature of the path of P (l) The Cartesian coordinates of the center of curvature of the path.{ Partial Ans: (b) 2.988 m/s; (d) θ,-139.7% (j) an-5.398 m/s, (1) xc=-0.4068 m) tangential com ponent a of the accele