What's the geometric reasoning behind e1, e2, and e3 being the first row of the matrix?
goldfish
Is the 2d cross product just used as a shortcut to get the area of the parallelogram?
lights
@lizard e1,e2,e3 are the vectors like x,y,z. It helps to denote the values in each axis for the resultant cross product vector.
yeeEeEet
why does the 2d cross product produce a scalar
nivek
u x v in the 2D sense seems to correspond to:
det[-u-]
[-v-]
Like goldfish I wonder what the application for this is.
samalex
@yeeEeEet I guess the cross product is only defined for 3d, so a 2d vector is appended with 0s. So the result is also 3d with the last element non-zero.
stroucki
The sqrt(det(...)) mumble really comes down to the magnitude of the cross product vector, according to wikipedia. And are the u, v and u x v arranged as row vectors for finding the determinant?
What's the geometric reasoning behind e1, e2, and e3 being the first row of the matrix?
Is the 2d cross product just used as a shortcut to get the area of the parallelogram?
@lizard e1,e2,e3 are the vectors like x,y,z. It helps to denote the values in each axis for the resultant cross product vector.
why does the 2d cross product produce a scalar
u x v in the 2D sense seems to correspond to: det[-u-] [-v-]
Like goldfish I wonder what the application for this is.
@yeeEeEet I guess the cross product is only defined for 3d, so a 2d vector is appended with 0s. So the result is also 3d with the last element non-zero.
The sqrt(det(...)) mumble really comes down to the magnitude of the cross product vector, according to wikipedia. And are the u, v and u x v arranged as row vectors for finding the determinant?