Find parametric equations for the tangent line at the point
on the curve
$\displaystyle r'(t)=-sin(t)i+cos(t)j+k$Find the parametric equation of the line tangent to
$\displaystyle r(t)=cos(t)i+sin(t)j+tk$ at the point $\displaystyle t=\frac{\pi}{3}$.
$\displaystyle ||r'(t)||=\sqrt{sin^{2}(t)+cos^{2}(t)+1}=\sqrt{2}$
The unit tangent vector is:
$\displaystyle T(t)=\frac{r'(t)}{||r'(t)||}$
Then sub in $\displaystyle t=\frac{\pi}{3}$
Use the direction numbers and the point $\displaystyle (x_{1},y_{1},z_{1})$ to find the parametric equations of the line.