Consider the Curve $\vec { r } ( t ) = \left( 2 t ^ { 2 } + 1 \right) \vec { i } + \left( t ^ { 2 } + 1 \right) \vec { j } + t \vec { k }$

True/False

Consider the curve $\vec { r } ( t ) = \left( 2 t ^ { 2 } + 1 \right) \vec { i } + \left( t ^ { 2 } + 1 \right) \vec { j } + t \vec { k }$ Does the curve lie on the parametric surface $x = s ^ { 2 } + t ^ { 2 } , y = s ^ { 2 } , z = t ?$