Motion in Space In Exercises 9-14, r(t) is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then find the par- ticle's speed and direction of motion at the given value of t. Write the particle's velocity at that time as the product of its speed and direction. t = 1 9. r(t) = (t + 1)i + (t² − 1)j + 2tk, √2 - t3 j + k, t = 1 3 (2 cos t)i + (3 sin t)j + 4tk, t = π/2 10. r(t) +2 = (1 + t)i + 11. r(t) = 12. r(t) 4 = (sec t)i + (tan t)j + 3ºk, t=π π/6 12. 13. r(t) = (2ln (t + 1))i + t²j + -k, t = 1 14. r(t) = (e)i + (2 cos 3t)j + (2 sin 3t)k, t = 0 In Exercises 15-18, r(t) is the position of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t = 0. 15. r(t) = (3t+ 1)i + √√√3tj + t²k 16. r(t) = (V21) i + (V21 – 161²) j t 17. r(t) = (In(t² + 1))i + (tan¯¹ t)j + √√ t² + 1 k