Question

how to find the cross product of four dimensional vector

Answer 1

Answer:

the dimensions are of physical.

and also realated to maths

Answer 2

Answer:

Step-by-step explanation:

This response relies on the property that the cross product of two vectors should return a third perpendicular vector, and only explains why 2,4,5 and 6 don't work.

Dimensions 0 and 1 have trivial cross products.

Consider 2d space. Two vectors don't have a third perpendicular vector, because there aren't enough dimensions!

Three is perfect. For any two vectors, you can find a third that is perpendicular.

Now suppose you have more dimensions. So there is a new vector that is perpendicular to each of the x,y,z axes. (This implies at least 4d). Call it w.

The cross product of x and w results in a new vector that is perpendicular to x and w. In fact it is perpendicular to y and z too! S the dim is at least 5 because of this vector xxw. The cross product of y and w generates a new dimension, and so does the cross product of z and w.

So we have 7 dimensions already:

x, y , z, w, xxw, yxw, zxw are all orthogonal.

We skip 4,5 and 6 because from 3D as soon as we increase the dimension by 1 (3-->4), we needed to add another dimensions for each dimension we already had (3+1+3=7).