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Slides/Video
dot product.mp4DOT PRODUCT
DOT PRODUCT
The dot product is used to determine the extent to which two vectors point in the same direction.
Or, if solving for 𝛳, it will tell you the angle between two vectors.
When is the dot product used?
When is the dot product used?
Physics: Calculating Work Done on an Object
Game Development: Reflection of Light
Machine Learning: Find Similarity of Two Data Points
Recommendation systems
Facial comparison software
2D Soccer Kick
2D Soccer Kick
Change v0 (velocity) and theta (kick angle) and watch how the dot products (green arrows) change.
CROSS PRODUCT
CROSS PRODUCT
cross product.mp4Cross product formula between any two vectors gives the area between those vectors and the magnitude of the resultant vector perpendicular to them.
When is the cross product used?
When is the cross product used?
Physics: Angular momentum
Astronomy: position and momentum of planet to determine its orbit
Wind & Ocean Currents
Sports: Find Football/Baseball Trajectory
Or any object spinning!
Curveball from above
Curveball from above
Change the direction, velocity, and spin on the ball and watch its trajectory change! Pay attention to which direction the arrows are going on different frames!
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