How can I plot a unit vector in 3-D space?

Hello everyone,

I need help in plotting a 3-D unit vector. I was trying to use the "quiver3" command but could n't succeed. Any help or useful suggestions in this regard would be highly appreciated.

The details are:

I have a vector “r” with three components “x”, “y” and “z”. By definition, the unit vector of any vector is that vector divided by its magnitude. What I need to obtain is the corresponding unit vector in 3-D space in terms of arrows spread over x, y, and z coordinates.

Thanks.

clear all
close all
clc
N=101;
x=linspace(-10,10,N);
y=x;
z=y;
for i=1:length(x)
    for j=1:length(y)
        for k=1:length(z)
          r_vec(i,j,k)=x(i)+y(j)+z(k);
          r_mag(i,j,k)=sqrt(x(i).^2+y(j).^2+z(k).^2);
          r_unit(i,j,k)=r_vec(i,j,k)./r_mag(i,j,k);
        end
    end
end

Answer 1

[KSSV]

You need not to use that complex, time consuming loop to get what you want.

clear all
close all
clc
N=101;
x=linspace(-10,10,N)';
y=x;
z=y;
r_vec = [x y z] ; 
r_mag = sqrt(x.^2+y.^2+z.^2) ; 
r_unit = r_vec./r_mag ; 

quiver3(x,y,z,r_unit(:,1),r_unit(:,2),r_unit(:,3))

[NaviKan]

@ KSSV thanks for your help but still there is a problem in the code. There is a dimension mismatch between r_vec (101X3 ) and r_mag (101X1 ) ,and thus r_unit=r_vec./r_mag does not work. Did you run the code and get the result?

[KSSV]

Did you run the code?

A vector in 3D should have three components so the size 101*3 is correct. Magnitude is length of the vector, so it will be 101*1. We divide each component with this magnitude. Again r_unit will be a unit vector and it shall have three components so it;s size is 101*3. To check you can find the magnitude of r_unit, you will get all 1's.

u_mag =  sqrt(r_unit(:,1).^2+r_unit(:,2).^2+r_unit(:,3).^2) ; 

The code is all right. It works.

[NaviKan]

Ok, thanks a lot.

It works and agian thanks for your help.