The rectangular equation for the parametric surface $x ( u , v ) = u$ $y ( u , v ) = v$ and $z ( u , v ) = \frac { v } { 3 }$ is

A) $y = 3 x$
B) $y = - \frac { z } { 3 }$
C) $y = - 3 z$
D) $y = 3 z$
E) $y = \frac { z } { 3 }$

Question

The rectangular equation for the parametric surface $x ( u , v ) = u$ $y ( u , v ) = v$ and $z ( u , v ) = \frac { v } { 3 }$ is

A) $y = 3 x$
B) $y = - \frac { z } { 3 }$
C) $y = - 3 z$
D) $y = 3 z$
E) $y = \frac { z } { 3 }$

Quizplus · Accepted Answer

The parametric equations are $x = u$, $y = v$, and $z = \frac{v}{3}$. Solving for $v$ in terms of $z$, we get $v = 3z$. Substituting $v = 3z$ into $y = v$, we get $y = 3z$.

The Rectangular Equation for the Parametric Surface x(u,v)=ux ( u , v ) = ux(u,v)=u

The Rectangular Equation for the Parametric Surface $x ( u , v ) = u$