Intuition for the Dot Product and the Cross Product

Often, we know how to solve things by formulas and we accept whatever was given to us. One thing we are forgetting is that these formulas actually mean something. The video below is a great example how to break in to learners that mathematical abstractions are more than just patterns..

Dot product intution:

One of the main point is how the dot product measures how much two vectors go in the same direction. Sal  did just dot.



 

Cross product intuition

The second topic of this video is how the cross product measures how much two vectors are perpendicular to each other. He also explained how the length of the cross product equals the area of the parallelogram the two vectors create.



One thing Sal could have added to this video is why we get negative values. Well, he might have had left that undiscussed for the viewer to think about.



Full video:

Cross and Dot Product intution