The discussion centers on the proof of the matrix formula for the cross product, specifically the relationship ||A X B|| = ||A|| ||B|| sin(θ). Participants clarify that the matrix formula serves as a mnemonic device for computing the cross product in Cartesian coordinates. The vector cross product is defined as A x B = (|A||B| sin(θ)) u, where u is a unit vector perpendicular to both A and B, determined by the right-hand rule. The conversation references resources such as Khan Academy and a tutorial from Michigan State University for further understanding.
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What do you mean by "matrixx formula"?prashant singh said:Is there any proof for the matrixx formula of the cross product. I am asking this because I have seen many videos and they have used the matrixx formula and then proved that ||A X B|| = ||A|||B||sin(theta), khan academy also used the same method
Sorry, this isn't the definition of the cross product A x B. It's the definition of the magnitude or norm of A x B; i.e., |A x B|.jedishrfu said:Vector cross product is defined as AxB = |A||B|sin(theta) where theta is the angle between A and B.
In the pdf in the link, the author never gives a geometric definition of the cross product. This product could be defined as A x B = (|A||B| sin(θ)) u, where u is a unit vector that is perpendicular to both A and B. The orientation of u can be determined using the right-hand rule (i.e., if you let the fingers of your right hand curl around from A to B, your thumb will point in the direction of u).jedishrfu said:Here's a small tutorial on it:
http://users.math.msu.edu/users/gnagy/teaching/11-fall/mth234/l04-234.pdf