Think of vec$(r)(t)=($:$6,4t,t^3$:$)$ as sweeping out the path of a particle over time.

a$)$ What is the location of the particle at $t=2?$ Give your answer as an ordered triple or vector.

b$)$ In what direction is the particle heading at $t=2?$ Give your answer as a vector.

c$)$ How fast $($assume meters per second$)$ is the particle moving in the $z-$direction at time $t=2?$