Answer
$x=-t; y=1; z=-2t$
Work Step by Step
We know that the velocity and acceleration is defined as: velocity is given as: $v(t)=r'(t)$ and acceleration is given as: $a(t)=v'(t)$
Now,
$v(t)=\lt -\sin t, \cos t, 2\cos (2t)\gt \\ \implies v(\dfrac{\pi}{2})=\lt -1,0,-2\gt$
Thus, we have the velocity components $v_x=-1,v_y=0,v_y=-2$
Now, the parametric equations are as follows:
$x=(-1)t+(0)=-t; y=(0) (t)+(1)=1; z=(-2)(t)+(0)=-2t$
Thus, $x=-t; y=1; z=-2t$
