A parameterization of $2 x - 3 y + z = 5$ is

A) $x ( u , v ) = u$ $y ( u , v ) = v$ $z ( u , v ) = 5 - 2 u + 3 v$
B) $x ( u , v ) = u$ $y ( u , v ) = v$ $z ( u , v ) = 5 - 2 u - 3 v$
C) $x ( u , v ) = u$ $y ( u , v ) = v$ $z ( u , v ) = 5 + 2 u + 3 v$
D) $x ( u , v ) = u$ $y ( u , v ) = v$ $z ( u , v ) = - 5 - 2 u + 3 v$
E) $x ( u , v ) = u$ $y ( u , v ) = v$ $z ( u , v ) = - 5 + 2 u + 3 v$

Question

A parameterization of $2 x - 3 y + z = 5$ is

A) $x ( u , v ) = u$ $y ( u , v ) = v$ $z ( u , v ) = 5 - 2 u + 3 v$
B) $x ( u , v ) = u$ $y ( u , v ) = v$ $z ( u , v ) = 5 - 2 u - 3 v$
C) $x ( u , v ) = u$ $y ( u , v ) = v$ $z ( u , v ) = 5 + 2 u + 3 v$
D) $x ( u , v ) = u$ $y ( u , v ) = v$ $z ( u , v ) = - 5 - 2 u + 3 v$
E) $x ( u , v ) = u$ $y ( u , v ) = v$ $z ( u , v ) = - 5 + 2 u + 3 v$

Quizplus · Accepted Answer

The correct parameterization is $x(u,v) = u$, $y(u,v) = v$, $z(u,v) = 5 - 2u + 3v$ because substituting $x = u$, $y = v$, and $z = 5 - 2u + 3v$ into the equation $2x - 3y + z = 5$ satisfies the original equation.

A Parameterization Of 2x−3y+z=52 x - 3 y + z = 52x−3y+z=5

A Parameterization Of $2 x - 3 y + z = 5$