Step by Step Solutions

(Steps Shown) The parametrization r(t)=x(t)i+y(t)j+z(t)k, where x(t)= cos ^2(ω t) , y(t)= sin (ω t) cos (ω t) , z(t)= sin (ω t) ,

Question: The parametrization \(\vec{r}\left( t \right)=x\left( t \right)\mathbf{i}+y\left( t \right)\mathbf{j}+z\left( t \right)\mathbf{k}\), where

\[\begin{aligned} & x\left( t \right)={{\cos }^{2}}\left( \omega t \right) \\ & y\left( t \right)=\sin \left( \omega t \right)\cos \left( \omega t \right) \\ & z\left( t \right)=\sin \left( \omega t \right) \\ \end{aligned}\]

is a curve that lies on the surface of the unit sphere.

  1. Verify that the curve lies on the surface of a sphere of radius one centered at the origin.
  2. Find the tangent vector to the curve.
  3. Verify that
    \[\vec{r}\left( t \right)\cdot \vec{r}'\left( t \right)=0\]
  4. Is the motion uniform?

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


∴ Other downloads you may be interested in ∴

log in to your account

Forgot password?
Don't have a membership account?
REGISTER

reset password

Back to
log in

sign up

Back to
log in