Goal: Make a function that will guide a particle from the starting position through three hoops and then to the ending point. Details: 1. The particle must start at (2,2,0) , when t=t1 2. pass through three hoops of radius .5 a. Hoop 1 centered at (1,1,1) pointing in direction -1,0,0 b. Hoop 2 centered at (0,-1,2) pointing in direction -1,-1,0 c. Hoop 3 centered at (-2,2,1) pointing in direction 0,1,-1 3. finish it at the end point (0,2,0), when t=t2 . Design a continuous vector function with parameter t. The vector function may be piecewise defined or not, it can be smooth or not; but it must be CONTINUOUS! Designate the starting t value t1 and ending t value t2.