Explore the intricacies of planar dot products and their linear algebraic perspective in this 29-minute mathematics lecture. Delve into the Coloured spreads theorem, examining concrete examples of spreads across blue, red, and green geometries. Discover how quadrances can be geometrically interpreted as "squares" in each color-coded geometry. Learn about the Coloured spreads formula, analyze specific examples, and understand the geometrical significance of red and green spreads. Investigate red and green quadrances, and conclude with an examination of the quadrances as signed areas theorem. This comprehensive exploration of advanced trigonometric concepts is part of the WildTrig: Intro to Rational Trigonometry series by N J Wildberger.