# Unit Tangent Vector Calculator

The calculator will find the unit tangent vector to the vector-valued function at the given point, with steps shown.

Related calculators: Unit Normal Vector Calculator, Unit Binormal Vector Calculator

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Find the unit tangent vector for $\mathbf{\vec{r}\left(t\right)} = \left\langle 2 \sin{\left(t \right)}, 2 \cos{\left(t \right)}, 7\right\rangle$.

## Solution

To find the unit tangent vector, we need to find the derivative of $\mathbf{\vec{r}\left(t\right)}$ (the tangent vector) and then normalize it (find the unit vector).

$\mathbf{\vec{r}^{\prime}\left(t\right)} = \left\langle 2 \cos{\left(t \right)}, - 2 \sin{\left(t \right)}, 0\right\rangle$ (for steps, see derivative calculator).

Find the unit vector: $\mathbf{\vec{T}\left(t\right)} = \left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 0\right\rangle$ (for steps, see unit vector calculator).

The unit tangent vector is $\mathbf{\vec{T}\left(t\right)} = \left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 0\right\rangle$A.