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 $0$.

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 …

Jun 26, 2020 · 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 …

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 make …

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 we can set …

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 is also very …

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 $\mathbb {R}^3$.

Two vectors are parallel if the wedge product (and consequently the cross product) of the two vectors is zero. The given formula calculates the magnitude of the wedge product of two vectors in two …

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 should not …

Apr 1, 2023 · The dot product can be used to find the length of a vector or the angle between two vectors. The cross product is used to find a vector which is perpendicular to the plane spanned by …