2017年2月4日 · The main thing is that my professor asked for us to solve this without using the "determinant method." I have just started linear algebra, so I am still trying to understand determinants and the like. I am just wondering how it is possible to prove the cross product of two vectors with another method? Any help would be great!

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 $0$. Share Cite

2019年3月22日 · E. A. Abbott describes a 2D cross product nicely in his mathematical fantasy book "Flatland": Flatland describes life and customs of people in a 2-D world: in this universe vectors can be summed together and projected, areas are calculated, rotations are clock-wise or counter clock-wise, reflection is possible...

Thus, the cross product of two unit vectors $\vec{u}$ and $\vec{v}$ is itself a unit vector if and only if $\vec{u}$ and $\vec{v}$ are orthogonal, i.e. meet at right angles (this makes $\sin(\theta)=\sin(\frac{\pi}{2})=1$). As to the general interpretation of the magnitude of the cross product, see Wikipedia:

2022年7月16日 · Therefore, the cross product of the two normal vectors will be parallel to each of the two planes. Which means it will also be parallel to the common line shared by the two planes - their line of intersection. Proving it mathematically in your specific case is quite trivial, and you should be able to do it by following definitions. Just find ...

2016年2月15日 · The difference between an ordered pair of vectors and a tensor product of vectors is that if you multiply one of the vectors by a nonzero scalar and the other by the reciprocal of that scalar, then you get a different ordered pair but the same tensor product. $\qquad$ $\endgroup$ –

Find the magnitude/length of the cross product of two vectors. Related. 0.

2018年5月31日 · The cross product is also useful in other arenas, and once again, it's useful because the underlying physical reality has a non-commutative flavor. Note that I used "some" multiple times. We use the cross product where it makes sense. The cross product of any two arbitrary quantities that can be represented as three-vectors can readily be computed.

Look. 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 that idea fimilar. One can understand cross product in this way:imagine a line segment that makes colorful marks wherever it moves on a paper.

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 expect it to have properties analogous to the properties of ordinary multiplication. What the cross product really is is a Lie bracket.