Identify the surface by eliminating the parameters from the vector-valued function $\mathbf { r } ( u , v ) = 6 \cos v \cos u \mathbf { i } + 6 \cos v \sin u \mathbf { j } + 3 \sin v \mathbf { k }$
A) plane
B) sphere
C) paraboloid
D) cylinder
E) ellipsoid

Question

Quizplus · Accepted Answer

The given vector-valued function represents an ellipsoid. This can be seen by squaring and adding the components, which results in the equation $(x/6)^2 + (y/6)^2 + (z/3)^2 = 1$, matching the standard form of an ellipsoid.

Identify the Surface by Eliminating the Parameters from the Vector-Valued r(u,v)=6cos⁡vcos⁡ui+6cos⁡vsin⁡uj+3sin⁡vk\mathbf { r } ( u , v ) = 6 \cos v \cos u \mathbf { i } + 6 \cos v \sin u \mathbf { j } + 3 \sin v \mathbf { k }r(u,v)=6cosvcosui+6cosvsinuj+3sinvk

Identify the Surface by Eliminating the Parameters from the Vector-Valued $\mathbf { r } ( u , v ) = 6 \cos v \cos u \mathbf { i } + 6 \cos v \sin u \mathbf { j } + 3 \sin v \mathbf { k }$