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
The cross product matrix formula is a mathematical formula used to find the cross product of two vectors in three-dimensional space. It involves creating a matrix using the components of the two vectors and taking the determinant of that matrix to find the cross product.
The cross product matrix formula is derived from the properties of the cross product operation, such as being perpendicular to both vectors and having a magnitude equal to the product of the magnitudes of the two vectors times the sine of the angle between them.
Yes, the cross product matrix formula can be visually represented using the right-hand rule. The direction of the cross product is given by the direction of your right-hand thumb when your fingers are curled in the direction of the first vector and then the second vector.
No, the cross product matrix formula can only be used in three-dimensional space. In higher dimensions, the cross product operation is replaced by the wedge product, which is a more general operation.
The cross product matrix formula has applications in physics, engineering, and computer graphics. It is commonly used to calculate torque, angular momentum, and magnetic fields in physics, and to create 3D graphics in computer programming.