While it is feasible to compute a cross-product in four dimensions, the cross-product only has the orthogonality property in three and seven dimensional spaces.

The equation with $\sin\theta$ can help you to find $\theta$ once you know the cross product, its magnitude, and the magnitudes (or norms) of $\vec a$ and $\vec b$, but it won't help you find the …

Dec 28, 2023 · 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 …

Oct 21, 2020 · How does this result in a vector with the geometric properties of the cross-product? To begin, I claim that the "natural" form of the cross-product is not that of a vector, but instead that of a …

Jul 25, 2017 · Maybe keep in mind that the other two answers implicitly use the Hodge star operation (and also a basis) to compute the "cross product in higher dimension" through the formal determinant …

Mar 3, 2017 · The formula for the cross product is : $$ a \times b = \vert a \vert \vert b \vert \sin (\theta) n $$ One of the purposes of the cross product is to get a vector value that is at right angles to both the …

However, instead of columns, I usually write the vectors in rows and write out the cross product like an elementary school multiplication. Then the cross product is computed by ignoring the first, second, …

Mar 22, 2019 · 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 …

May 18, 2025 · 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 …

Sep 26, 2019 · Geometric explanation of the formula for double cross product [duplicate] Ask Question Asked 6 years, 2 months ago Modified 6 years, 2 months ago