Answer
Let $ \bf{C}$ be a smooth curve with position vector $r(t)$.
The tangent vector is $r'(t)$.The unit tangent vector is: $$T(t)=\dfrac{r'(t)}{||r'(t)||}$$
Vector equation of tangent line at $t=a$ is:
$s(u)=r(a)+u \cdot r'(a)$
Work Step by Step
Let $ \bf{C}$ be a smooth curve with position vector $r(t)$.
The tangent vector is $r'(t)$.The unit tangent vector is: $$T(t)=\dfrac{r'(t)}{||r'(t)||}$$
Vector equation of tangent line at $t=a$ is:
$s(u)=r(a)+u \cdot r'(a)$
