Parametric Motion Analysis Consider a particle moving along a parametric curve defined by: x$($t$)=3$cos$($t$)$ y$($t$)=2$sin$($t$)$ z$($t$)=$ t for t $0.$ Find the velocity and acceleration vectors at any time t$.$ Calculate the speed of the particle at t $=$ $/4.$ Determine the points where the particle's movement is perpendicular to the vector $<1,1,1>.$ Finally, derive an expression for the curvature of this path.