Identify the geometric object that is represented by parametric equations $\mathbf { r } ( t ) = \langle 3 \cos t , 3 \sin t , t \rangle$ .
A)A plane
B)A cone
C)A straight line
D)A circular cylinder
E)A circle
F)A circular disk
G)A helix
H)A sphere

Question

Quizplus · Accepted Answer

The parametric equations given describe a helix. The $x$ and $y$ components ($3\cos t$ and $3\sin t$, respectively) describe a circle of radius 3 in the $xy$-plane, while the $z$ component increases linearly with $t$, indicating a movement upwards or downwards along the $z$-axis as $t$ increases, thus forming a helix.

Identify the Geometric Object That Is Represented by Parametric Equations r(t)=⟨3cos⁡t,3sin⁡t,t⟩\mathbf { r } ( t ) = \langle 3 \cos t , 3 \sin t , t \rangler(t)=⟨3cost,3sint,t⟩

Identify the Geometric Object That Is Represented by Parametric Equations $\mathbf { r } ( t ) = \langle 3 \cos t , 3 \sin t , t \rangle$