Q9

Which of the equations best represent the curve below?

[Diagram: A three-dimensional spiral around the $z$-axis, with radius increasing as $|t|$ increases.]

(A) $\displaystyle \vec r(t)=(\cos t)\vec i+(\sin t)\vec j+t\vec k$

(B) $\displaystyle \vec r(t)=(t\cos t)\vec i+(t\sin t)\vec j+t\vec k$

(C) $\displaystyle \vec r(t)=(t\cos t)\vec i+(t\sin t)\vec j+\frac{1}{t}\vec k$

(D) $\displaystyle \vec r(t)=(\cos t)\vec i+(\sin t)\vec j+\frac{1}{t}\vec k$