Projection and distance of vectors - MATLAB

Hello,

I have two questions. For example I have two vectors u and v, and:

1. I have to calculate the distance between vectors u and v
2. I have to find the projection of u onto the line spanned by v

I have some ideas for the first one, dist(u-v) or just (u-v) but I am not sure if it is correct.

And for the second question I found the command in matlab that I could do it like this u=orth(v)

Can you please advise me if I am heading towards the right direction or am I completely clueless. :)

Thank you in advance Nina

Answer 1

[Matt J]

There is a function NORM for finding distances. There is also a function DOT for taking dot-products. As you know, dot-products play an important role in finding projections.

[William]

Matt, if you possibly still are active could you point me to where I can find out how to count projections? I've yet to see a helpful guide. Thanks!

[Matt J]

@William I dont know what it means to "count projections". It probably warrants a separate question.

[William]

@Matt J Honestly that's all the instructions I recieved for that part. At least I know my confussion isn't just me being an airhead.

Answer 2

[Roger Stafford]

 dot(u,v)*v/norm(v)

Answer 3

[Lea Nina]

Hi,

thank you for your prompt reply. Yes I know how to make dot product, but I don't know how to continue to get the projections. Do you maybe have any formula that I could use or at least if the above formulas are correct.

Thanks again Nina

[Image Analyst]

if one "vector" goes from 2,2 to 3,3 and the other vector goes from 11,11 to 15,15, do those vectors have a projection? Or do all your vectors have their tails at the same location? Is the "distance" between the vectors, the distance between their tips?

Answer 4

[Lea Nina]

So maybe I wrote wrong the first time, the exercise I have is like this: Given the vectors u=[1.7;4.3;-1.6;2.7;1.8;4.1] and v [4.4;-2.2;3.3;1.9;0.6;-2.5] (in Matlab these vectors would be in one column each).

So like I wrote before, the task says:

1. calculate the distance between vectors u and v 2. calculate the projection of u onto the line spanned by v

So I am really lost at this, so any help would be appreciated.

Thank you once again Nina

[Matt J]

You shouldn't still be lost now that you've been given the formulas and the code for the single vector case.

Answer 5

[Lea Nina]

Ops, didn't see those formulas. Thank you Roger!!!!!

[Matt J]

It is strange that you have never seen these formulas in a class where the homework exercises so abundantly require them.