Chapter 12 - Vector-Valued Functions - 12.1 Introduction To Vector-Valued Functions - Exercises Set 12.1 - Page 846: 34

True

The first two components, $2\cos t$ and $2\sin t$, describe a circle in the 2D plane. The third component is not constant, so it cannot represent a circle in 3D space. Since the third component varies linearly with $t$, it must represent a circular helix. (The third component lifts up the circular curve as $t$ increases.) Result: True