Describe the Similarities and Differences Between the Following Two Curves $\text { Curve 1: } \vec { r } ( t ) = ( 3 + 3 t ) \vec { i } + ( 1 - t ) \vec { j } + ( 3 + 4 t ) \vec { k } , - \infty \leq t \leq \infty \text {, }$

Essay

Describe the similarities and differences between the following two curves. $\text { Curve 1: } \vec { r } ( t ) = ( 3 + 3 t ) \vec { i } + ( 1 - t ) \vec { j } + ( 3 + 4 t ) \vec { k } , - \infty \leq t \leq \infty \text {, }$ $\text { Curve 2: } \vec { r } ( t ) = \left( 3 + 3 t ^ { 2 } \right) \vec { i } + \left( 1 - t ^ { 2 } \right) \vec { j } + \left( 3 + 4 t ^ { 2 } \right) \vec { k } , - \infty \leq t \leq \infty \text {. }$