Find a vector-valued function for the hyperboloid $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 121$
A) $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + \sqrt { u ^ { 2 } + 121 } \mathbf { k }$
B) $\mathbf { r } ( u , v ) = u \sin v \mathbf { i } + 11 u \cos v \mathbf { j } + \sqrt { u ^ { 2 } + 1 } \mathbf { k }$
C)$\mathbf { r } ( u , v ) = 11 u \sin v \mathbf { i } + u \cos v \mathbf { j } + \sqrt { u ^ { 2 } - 1 \mathbf { k } }$
D)$\mathbf { r } ( u , v ) = 11 u \cos v \mathbf { i } + 11 u \sin v \mathbf { j } + 11 \sqrt { u ^ { 2 } - 1 } \mathbf { k }$
E) $\mathbf { r } ( u , v ) = 11 u \cos \boldsymbol { i } + 11 u \sin v \mathbf { j } + 11 \sqrt { u ^ { 2 } - 121 } \mathbf { k }$

Question

Find a vector-valued function for the hyperboloid $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 121$ 
A) $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + \sqrt { u ^ { 2 } + 121 } \mathbf { k }$
B) $\mathbf { r } ( u , v ) = u \sin v \mathbf { i } + 11 u \cos v \mathbf { j } + \sqrt { u ^ { 2 } + 1 } \mathbf { k }$
C)$\mathbf { r } ( u , v ) = 11 u \sin v \mathbf { i } + u \cos v \mathbf { j } + \sqrt { u ^ { 2 } - 1 \mathbf { k } }$
D)$\mathbf { r } ( u , v ) = 11 u \cos v \mathbf { i } + 11 u \sin v \mathbf { j } + 11 \sqrt { u ^ { 2 } - 1 } \mathbf { k }$
E) $\mathbf { r } ( u , v ) = 11 u \cos \boldsymbol { i } + 11 u \sin v \mathbf { j } + 11 \sqrt { u ^ { 2 } - 121 } \mathbf { k }$

Quizplus · Accepted Answer

The correct parameterization for the hyperboloid $x^2 + y^2 - z^2 = 121$ is $\mathbf{r}(u, v) = 11u \cos v \mathbf{i} + 11u \sin v \mathbf{j} + 11\sqrt{u^2 - 1} \mathbf{k}$, which satisfies the equation when substituting $x = 11u \cos v$, $y = 11u \sin v$, and $z = 11\sqrt{u^2 - 1}$.

Find a Vector-Valued Function for the Hyperboloid x2+y2−z2=121x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 121x2+y2−z2=121

Find a Vector-Valued Function for the Hyperboloid $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 121$