In BC calculus the only application parametric equations and vectors is motion in a plane. Polar equations concern area and the meaning of derivatives. See the review notes for more detail. (only 3 items here)
Motion Problems: Same Thing Different Context (11-16-2012)
Implicit Differentiation of Parametric Equations (5-17-2014)
A Vector’s Derivative (1-14-2015)
This is a series of posts that could be used when teaching polar form and curves defined by vectors (or parametric equations). They might be used as a project. Hopefully, the equations that produce the graphs will help students understand these topics. Don’t let the names put you off. Except for one post, there is no calculus here.
Rolling Circles (6-24-2014)
Epitrochoids (7-1-2014) The most common of these are the cycloids.
Hypocycloids and Hypotrochoids (7-7-2014)
Roulettes and Calculus (7-11-2014)
Roulettes and Art – 1 (7-17-2014)
Roulettes and Art – 2 (7-23-2014)
Type 8: Parametric and Vector Equations (3-30-2018) Review Notes
Type 9: Polar Equation Questions (4-3-2018) Review Notes