Question

Consider the curve parameterized by
r(t)=⟨tsin(t),tcos(t),t⟩ for −[infinity]

Answer 1

A curve parameterized by r(t)=⟨tsin(t),tcos(t),t⟩ represents the path of a particle in 3D space. The vector function r(t) gives the position of the particle at time t. The curve can be visualized as a spiral that expands away from the origin as t increases.

Step-by-step explanation:

A curve parameterized by r(t)=⟨tsin(t),tcos(t),t⟩ represents the path of a particle in 3D space.

The vector function r(t) gives the position of the particle at time t. The x-coordinate of the position vector is given by r_x(t) = tsin(t), the y-coordinate is given by r_y(t) = tcos(t), and the z-coordinate is given by r_z(t) = t. The curve can be visualized as a spiral that expands away from the origin as t increases.