Consider the parametric surface $\vec { r } ( s , t ) = s \sin \left( \frac { \pi } { 2 } \right) \vec { i } + s \cos \left( \frac { \pi } { 2 } \right) \vec { j } + 2 t \vec { k }$ Does it contain the point (0, -3, -4)?

Question

Quizplus · Accepted Answer

The surface is a plane parallel to the xy-plane, so it does not contain any points with a non-zero z-coordinate.

Consider the Parametric Surface r⃗(s,t)=ssin⁡(π2)i⃗+scos⁡(π2)j⃗+2tk⃗\vec { r } ( s , t ) = s \sin \left( \frac { \pi } { 2 } \right) \vec { i } + s \cos \left( \frac { \pi } { 2 } \right) \vec { j } + 2 t \vec { k }r(s,t)=ssin(2π​)i+scos(2π​)j​+2tk

Consider the Parametric Surface $\vec { r } ( s , t ) = s \sin \left( \frac { \pi } { 2 } \right) \vec { i } + s \cos \left( \frac { \pi } { 2 } \right) \vec { j } + 2 t \vec { k }$