Wireless sensing, tracking, and drawing technologies are enabling exciting new possibilities for human-machine interaction. They primarily rely on measurements of backscattered phase, amplitude, and Doppler signal distortions, and often require many measurements of these quantities---in time, or from multiple antennas. In this paper we present the design and implementation of PolarDraw, the first whiteboard in the air that sends differentially-polarized wireless signals to glean more precise tracking information from a tag. Leveraging information received from each polarization angle, our novel algorithms infer orientation and position of an RFID-tagged pen using just two antennas, when the user writes in the air or on a physical whiteboard. An experimental comparison in a cluttered indoor office environment compares two-antenna PolarDraw with recent state-of-the-art object tracking systems that use double the number of antennas, demonstrating comparable centimeter-level tracking accuracy and character recognition rates (88--94%), thus making a case for the use of polarization in many other tracking systems.