Identify the type of parametric surface produced by the parametric vector functionr(u,v)=⟨2sinucosv,2sinusinv,2cosu⟩r(u,v)=⟨2sin⁡ucos⁡v,2sin⁡usin⁡v,2cos⁡u⟩ with 0≤u≤π2,0≤v≤π20≤u≤π2,0≤v≤π2. **Identify the Type of Parametric Surface Produced by the Parametric Vector Function**\[ \mathbf{r}(u, v) = \langle 2 \sin u \cos v, 2 \sin u \sin v, 2 \cos u \rangle \] with \[ 0 \le u \le \frac{\pi}{2}, \; 0 \le v \le \frac{\pi}{2}. \]This surface is the portion of a sphere of radius $ \_\_\_\_\_\_ $ lying...- [ ] above the xy-plane- [ ] below the xy-plane- [ ] in the first octant- [ ] in the octant where x and z are positive but y is negative

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Identify the type of parametric surface produced by the parametric vector function

r(u,v)=⟨2sinucosv,2sinusinv,2cosu⟩r(u,v)=⟨2sin⁡ucos⁡v,2sin⁡usin⁡v,2cos⁡u⟩ with 0≤u≤π2,0≤v≤π20≤u≤π2,0≤v≤π2.

**Identify the Type of Parametric Surface Produced by the Parametric Vector Function**

\[ \mathbf{r}(u, v) = \langle 2 \sin u \cos v, 2 \sin u \sin v, 2 \cos u \rangle \]
with
\[ 0 \le u \le \frac{\pi}{2}, \; 0 \le v \le \frac{\pi}{2}. \]

This surface is the portion of a sphere of radius $ \_\_\_\_\_\_ $ lying...

- [ ] above the xy-plane
- [ ] below the xy-plane
- [ ] in the first octant
- [ ] in the octant where x and z are positive but y is negative

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