Linear Algebra 2g: Subtraction of Geometric Vectors

[terryphi]

finally, after 10 years, an intuitive explanation of vector subtraction!

[lalaland]

This is the best linear algebra course on Youtube but it was diffcult to find. Perhaps consider using more descriptive tags and title so your great course and website will be found by more people.

[compphysgeek]

I find it interesting that you say that all vectors originate from the origin. For me the "real" or physical vectors are the ones that don't origin from the origin. Let's look at the example A, B, and A - B.
A - B is a physical vector that describes for example the displacement from B to A. The origin is my reference point but I can place the reference point anywhere I want. I by choosing different reference points A and B will change, however, A - B won't change.

[antonellomascarello]

0:23 : first approach
2:15 : second approach
4:01 : note / reminder : all vectors in LA emanate from the origin
5:48 : in 3 dimensions

[mohammednabulsi]

very useful lectures,
still, I think maybe the second method vector's drawing should have a+b instead of a-b at the right side, not sure but wondering. wish that I can share an Image.

[koningen]

Thanks for all your efforts. Although I'm not able to respond much do the time constraints, I'm still watching and think you are a very good instructor and the insights you give us are very important. I have a question for you nobody can give me a satisfactory answer to. It has nothing to do with the subject you are teaching us at the moment but I think you are the only one to come up with an answer. In Cartesian coordinates we have the order (x, y) and usually y is a function of x. Now in polar coordinates the order is (r, theta) and r is usually a function of theta so the order is reversed. Why is that? I cant believe that is just an oversight, there must be a deeper reason for it. This bugs me. Please help.

[AbhishekYadav-dedy]

Borishenko's book is one of the reference given in your Tensor book. In its first chapter three types of vectors are defined free, sliding and bound vectors. Consider the case of bound vectors which are fixed at  particular locations. How can we define the subtraction or addition of these vectors because for defining the addition/subtraction of two vectors we need to bring them closer (tip to And if we can't do that then it means we can't define the subtraction and similarly we can't define the differentiation of the bound vectors. I can only think of a forced transport of these vectors (to use tip to tail thing)(and then transport theorem come into picture) for defining the addition/subtraction and that's when everything gets very complicated. Can you please make a video to explain these things.
Thanks and Regards

[mee_shh]

the -b vector in the first diagram is in the opposite direction of -b vector in the second diagram ?!!