The position of a particle in the xy-plane at time t is r(t) = (t+ 1)i + (!" - 2)j. Find an equation in x and y whose graph is the path of the particle. Then find the particle's velocity and acceleration vectors at t = 3 The equation for the path of the particle is y =. The equation r(t) = (3 sin t) i + (4 cos t) j + (3t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t= 2x as a product of its speed and direction. The velocity vector is v(t) = ( i + () j + ( ) k. The equation r(t) = (2t + 3)1 + (15t) j+ (21") k is the position of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t = The angle is radians. (Type an exact answer, using x as needed.) Show that the vector-valued function shown below describes the motion of a particle moving in a circle of radius 1 centered at the point (3,2,4) and lying in the plane 2x + 2y - 4z= -6. r(t) = (31+2)+ 4k) + cost 12' 12 + sint 1 13 3 V3 First write the three parametric equations for x, y, and z. What is the parametric equation for x? x =[ (Type an exact answer, using radicals as needed.)