Question

Can somebody prove the cross product for me please?

Answer 1

And how it produces an orthogonal vector

Answer 2

Or how we can use it to find an angle or the area of a paralleogram

Answer 3

My wording might be a bit vague but I am talking about these kinds of cross products right here: http://mathworld.wolfram.com/CrossProduct.html

Answer 4

i hope u r talking about vector cross product ..

Answer 5

I think you're talking about calculating it from a special matrix?

Answer 6

I am currently taking Multivariable Calculus and the vector cross product is pretty the only one that I am exposed to and I'm curious as to how it works visually.

Answer 7

vector cross product defines a vector which is perpendicular to the plane containing the two vectros whose cross product u r to determine... mathematically it is defined as AXB = n |A||B|sin(angle between the given vectors) n is the unit vector in the plane containing the vectors A and B area of parallelogram is given by |AXB|= |A||B|sin(angle between the given vectors)

Answer 8

you still there?

Answer 9

I thank Matricked for his or her answer, but I'm more of emphasizing as to why solving a cross product would give me orthogonal vectors, angles, or area. I've done many problems with the cross product but I'm often left wondering why how does using a matrix give me the orthogonal vector or why I would get area. I'm more of asking for visual cues and a proof as to why the cross product works as it does.

Answer 10

the reason it's orthogonal is because it's an area VECTOR. Vector representations of area must be orthogonal to the surface element they define.

Answer 11

ie you have magnitude |axb| equal to the unsigned area of the //gram defined by ab.

Then the cross is defined as the signed area given by the screw rule or equivalent.