Find the Unit Tangent and Unit Normal Vectors $\mathrm { T } ( t )$

Essay

Find the unit tangent and unit normal vectors $\mathrm { T } ( t )$ and $\mathrm { N } ( t )$ for the curve $C$ defined by $\mathbf { r } ( t ) = t \mathbf { i } + 2 t ^ { 2 } \mathbf { j }$ . Sketch the graph of $C$ , and show $\mathbf { T } ( t )$ and $N ( t )$ for $t = 1$ .