The following equations represent a curve or a surface.Select the best geometric description. (Note: $\rho$, $\varphi$, $\theta$ are spherical coordinates; r, $\theta$, z are cylindrical coordinates.) $x = t , y = 2 t , z = 3 t , 0 \leq t \leq 10$
A)Part of a line through the origin
B)Part of a cylinder.
C)Part of a cone.
D)Disk

Question

Quizplus · Accepted Answer

The given equations $x = t$, $y = 2t$, $z = 3t$ represent a line through the origin in 3D space, where $t$ is a parameter that varies. The coefficients of $t$ (1, 2, 3) indicate the direction of the line, and since all three variables are directly proportional to $t$, it confirms the geometric figure is a line, not a surface.

The Following Equations Represent a Curve or a Surface ρ\rhoρ φ\varphiφ

The Following Equations Represent a Curve or a Surface $\rho$ $\varphi$