The dot product measures projection
An animation shows a vector drawn as a blue arrow with its scalar projection labeled |a| cos theta in red text along the horizontal axis. The label sits just clear of the y-axis for readability while still meeting the projection point, and the motion is paced slowly so viewers can track how the projection length changes as the vector's angle changes. Useful for introducing dot products, components, and trigonometric projection to students.
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. - Almost there, just that |a| cos theta red text should be a tiny bit to the right to not touch the y-axis
Make the next one in this series
- Animate the same setup showing |a| sin theta as the vertical projection onto the y-axis.
- Show two vectors and animate how the dot product equals |a||b| cos theta between them.
- Create a version where theta increases continuously and a graph plots cos theta versus the projection length.
