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 $t = 1$.

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The Answer of 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 $t = 1$.

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

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