Anyone here understand how a cross product works in relation to 3D ? I understand the core of what it does which is the third vector from the other two vectors but relating that to 3D space has been the issue. Here is my theory of how it works, suppose you have a sphere and a plane in a scene, the sphere is traveling on the Y axis, that is one vector, the plane is static, which is another vector, the X axis. When the sphere touches or hits the plane, the cross product would be the axis or vector to the right of the sphere and plane, suppose that is behind the sphere, when the sphere touches the plane, it will create a red mark which is the cross product of the sphere and the plane ?
Is my theory somewhat correct, or completely wrong ?
We represent a complex number in XY plane. real part is along or parallel to X axis and imaginary part is along or parallel to Y axis.e.g. Let us say you represent a land map as complex plane.say village B is x+jy distance from village A. x is distance along east ( displacement to west considered -ve)and y along north. You can cover the distance by 3 sessions of drive say. a+jb, c+jd, e+jf Thenat the same distance.
Real and imaginary parts must separately balance on both sides.
i.e. x=a+c+e and y=b+d+f If both are not satisfied you will not reach B.
If there is a village C such that AC=j(x+jy) ,C will be located such that
You're going to have to give a simpler example, until I can wrap my head around it ?
usually mathematicians use i and engineers use j . Both mean the same thing. 4+5i is represented by distance 4 along x axis and distance 5 parallel to y axis.You can say an "i" attached with a number rotates the vector by 90^0.
interestingly 4 i^2 means vector 4 along x axis is rotated by 180^0 and becomes -4 . this tallies with the concept that i^2=-1.
What if I write a formula 34j, what is that, literally, besides the number 34 ?
If someone asks you, what is the dimensions of the hair dryer, you could tell them the height and the width of the part you hold; you could then measure the height and width of the part in which the air comes out, then again, you could just tell them the volume in which the hair dryer occupies. No the handle is not, suppose 5.2" but the part in which the air is released, is 5.2".
You can not simply derive measurements such as height, width, and depth for a complicated shape such as a human body or car with more data. Even if you had this data, its extremely difficult to do. If your object was simple such as a cube, cylinder, or triangle and had more data,... we could calculate this a lot easier.
Not knowing any more than just the SA of say a box,... we can derive dimensions for say a box but there are infinitely many dimensions. This means the box can be of any shape or even size. If you give us the SA, L, and W, we can calculate the depth for example. If you only give the SA and L, that would mean the width and depth would be infinite.
I understand. A program I use only gave me those measurements from a irregular object, the program must be getting the information some how, some way, that is what I want to know ?
We both can agree that the program is not spitting out a random value for the surface area of the object !