The equation r(t) = (2t + 4) i + (t2 - 7) j + (t) is the position of a particular in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t = 1 as a product speed and direction. What is the velocity vector? What is the acceleration vector? Write the velocity vector at t = 1 as a product of the speed and direction. (Type exact answers, using radicals as needed.) The equation r(t) = (6 cos t) i + (2 sin t) j + (t) 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 = 0 as a product of its speed and direction. The velocity vector is The acceleration vector is velocity vector at t = 0 written as a product of the speed and direction is (Type exact answers, using radicals as needed.) The equation k is the position of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t = 0. What is the angle? (Type an exact answer, using n as needed.)