Understanding the definition of the cross product The third constraint is used as a trick to fill out the system of equations so that it can be solvable for three unknowns, so we just define the length of the cross product will be of unit length
Proof of the cross product formula - Mathematics Stack Exchange Since the cross-product formula follows the right-hand rule for the basis vectors, all other vectors that are a linear combination of these will also follow the right-hand rule This follows from the rules for associativity when multiplying with a scalar and the distributivity of the cross product over vector addition
intuition - What is the intuitive way to understand Dot and Cross . . . The cross product has two purposes The magnitude of the vector $\vec a \times \vec b$ is the magnitude of the rejection of $\vec a$ from $\vec b$ times the magnitude of $\vec b$ (compare this to the dot product which gives the magnitude of the projection times distance) And its direction is perpendicular to both $\vec a$ and $\vec b$
Why is cross product defined in the way that it is? At a really basic level we want the cross product to take two vectors and give us a vector perpendicular to both Clearly we have two choices in non-degenerate cases, and choosing the "right hand rule" is just a matter of convention You can equally well take the left hand rule, but this is just multiplying the usual cross product by $-1$
linear algebra - How does computing the determinant of a matrix with . . . This definition of the cross product is definitely degrading the notion of determinant, and should be abolished Outside of "Schaum's Outline" (which was outdated even when I was a student in the fifties of the last century), and similar texts, all elements of a matrix should be of the same type
Whats the cross product in 2 dimensions? [duplicate] Point for you to ponder on - the cross product of two vectors gives a third vector, perpendicular to the original two vectors Could you define a (meaningful) cross product in R^2 that would imitate that property?
Definition of cross product - Mathematics Stack Exchange The R naming is not standard and does not correspond to the usual cross-product operator between 3D vectors IMO, coproduct or transproduct would have been a better idea
Visual Ways to Remember Cross products of Unit vectors? Cross-product . . . Then the cross product is computed by ignoring the first, second, third columns in order; computing the corresponding $2 \times 2$ determinant; and negating the middle term [which really just amounts to using the determinant mnemonic, but involves less writing]
Connection between cross product and determinant When I calculate a cross product of two vectors in Cartesian coordinates, I calculate something that seems like the determinant of a 2x2 matrix Is there any connection between the determinant and