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 …

Sep 25, 2015 · The vectors and their cross product live in a coordinate-free space, just floating around. We're just imposing coordinates to make concrete calculations simpler.) That means …

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 …

Answer So the answer to your question is that the cross product of two parallel vectors is $\mathbf 0$ because the rejection of a vector from a parallel vector is $\mathbf 0$ and hence has length …

Apr 12, 2011 · The name "product" for the cross product is unfortunate. It really should not be thought of as a product in the ordinary sense; for example, it is not even associative. Thus one …

Jun 14, 2013 · I'm not a mathematician, but I have a perspective which can explain why the cross product of two vectors is another vector perpendicular to them. It is not a proof but it will help …

Oct 12, 2015 · This is a completely false and misleading answer. You can't expect to do linear algebra with a curvilinear coordinate system. E.g. using this determinant, a simple cross …

Jul 25, 2017 · Whenever you wedge vectors together, the result equals zero if at least two of the factors are linearly dependent. Think of what happens to the cross product in $\mathbb {R}^3$.

Every time you come up with a question like this, the very very first thing you have to do is to consider examples. It is very easy to construct unit vectors, and when you have two of them, it …

Feb 8, 2016 · The overdot notation I used here is just a convenient way of not having to write out components while still invoking the product rule. When you differentiate a product in single …