The dot product measures projection
This animation shows vectors a=(3,1) and b=(2,2) plotted on a grid, with the projection of a onto b highlighted along the blue arrow representing b. The red label |a|cos(theta) marks the projection length where it touches the blue vector, visually linking the geometric projection to the algebraic dot product formula. Viewers see how a·b = |a||b|cos(theta) equals a1b1+a2b2 = 8, yielding theta approximately 26.6 degrees. Useful for students learning vector geometry and trigonometric interpretation of dot products.
16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Apply ALL of the following review notes precisely; keep everything else identical. This video is for social media and must be impeccable. - |a| cos theta red text, touches blue arrow. Animation, should be a bit slower overall
Make the next one in this series
- Show the projection formula extended to 3D vectors with a rotating coordinate system
- Compare orthogonal projection versus vector rejection using the same two vectors
- Demonstrate how the dot product determines whether two vectors are acute, right, or obtuse
