The equation

r(t)=(12sint)i+(5cost)j+(4t)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=

as a product of its speed and direction.

The velocity vector is

v(t)=enter your response here

i+enter your response here

j+enter your response here

k.

Part 2The acceleration vector is

a(t)=enter your response here

i+enter your response here

j+enter your response here

k.

Part 3The velocity vector at

t=

written as a product of the speed and direction is

v()=enter your response here[enter your response here

i+enter your response here

j+enter your response here

k].

(Type exact answers, using radicals as needed.)