Apr 1, 2023 · What purposes do the Dot and Cross products serve? Do you have any clear examples of when you would use them?

Jun 14, 2013 · The cross-product is then orthogonal to $\mathbf {a}$ and $\mathbf {b}$, roughly, because the direction perpendicular to both vectors is the one that maximizes the volume.

What am I missing? Although this post is very useful for explaining the logic behind cross products What is the logic/rationale behind the vector cross product?, it didn't contain enough relevant …

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 …

In three dimensions this 'cross product' is a vector; in two dimensions it's just a number. In fact, it's the determinant of the 2x2 matrix you get from considering v1 and v2 as a basis. Thinking of it …

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 …

Nov 7, 2013 · Integral with cross product Ask Question Asked 12 years, 1 month ago Modified 12 years, 1 month ago

Dec 7, 2013 · As you note, each coordinate of the cross product is the (signed) area of the parallelogram spanned by the projections of $\bf {v}$ and $\bf {w}$ to each coordinate plane …

Mar 15, 2023 · If $ (1,0,0)$ and $ (0,1,0)$ are ordinary vectors, then their cross product $ (0,0,1)$ can be treated as a pseudovector, which gets an extra factor of $-1$ on reflection, therefore …

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 …