00:02
If a curve is in a plane is the binormal vector a constant, and that's true.
00:10
And you can go through and kind of show it mathematically, whether it's kind of just a lot of algebra.
00:18
So i'm just going to kind of go through why you know that.
00:21
So if you have a curve that's in a plane, so no matter what plane it is, it's in this plane, the tangent will be in that plane, because there's no, you know, you can always define this plane.
00:36
So whatever plane it is, know how, i matter how skewed it is, you can always define an x and y axis in it and then a z axis out of it.
00:46
So you know that then the tangent and the normal vectors have got to be in that plane because there's no component of that curve coming out of the plane.
00:58
So if you take derivatives, then you'll never get a component of these that's out of that plane.
01:06
But then you know that the cross -product, which is a unit vector, must be out of the plane because the cross -product of two vectors that are in the same plane that are orthogonal to one another and also unit vectors is a unit vector out of that plane...