Find a new ortonormal coordiante vectors with a point and vector given

Hi, for an university problem, I have to find a new tern with the origin in the point P1=[2 2 1], the z axis oriented along the vector N=[1 1 2] and with the x and y axes belonging to the plane passing through point P1 and identified from the normal N. I also have to make it's graphic representation, with red color for the x axis, green for y and blue for z. All that I can manage to do was using null space

clc;

clear all;

P1=[2 2 1];

N=[1 1 2];

VN=N/norm(N);

BVN=null(VN);

NV=[BVN(:,1) BVN(:,2) VN'];

[Torsten]

What do you mean by "tern" ?

[Federico Cotugno]

[Torsten]

3 orthonormal coordinate vectors one of which is [1 1 2]/sqrt(6) ?

Add

null([1 1 2])

ans = 3×2

-0.4082 -0.8165 0.8816 -0.2367 -0.2367 0.5266

[Federico Cotugno]

Yes, i have to find 3 ortonormal coordiante vectors that have the origin in the point P1 and one of this axis is the along the vector N. I think that with my code I've found the 3 coordinate but i don't know how to make them start from P1 and how to plot it

[Torsten]

Hint: Use quiver3.

[Federico Cotugno]

I'm trying but i'm stuck

[Federico Cotugno]

I tried this but obv is not right

clc;

clear all;

N=[1 1 2];

VN=N/norm(N);

BVN=null(VN);

a=[1 1 1]

NV=[BVN(:,1) VN' BVN(:,2) a'];

q=[1 0 0 1;0 1 0 2;0 0 1 2;0 0 0 1]

t=NV';

b=q*t;

B=b';

Q=[b(:,1),b(:,2),b(:,3)];

plot3(Q(:,1),Q(:,2),Q(:,3));

[Federico Cotugno]

Also tried this,it seems a bit better but i don't think is good

clc;

clear all;

N=[1 1 2];

VN=N/norm(N);

BVN=null(VN);

NV=[BVN(:,1),BVN(:,2),VN'];

P1=[2 2 1];

NV1=P1.*NV;

T=NV1';

plot3(T(:,1),T(:,2),T(:,3))

Answer 1

[Brahmadev]

Hi Federico,

I understand that you would like to get two vectors normal to the given vector originating at P1 = [2 2 1] towards N = [1 1 2]. If we assume a random vector, say, towards N1 = [1 1 3] from P1, we can get their cross-product to find a vector that is normal to P1N. If we further take the cross-product of P1N and P1N1, we can get the third vector which will be normal to both these vectors. This can be chosen as our third co-ordinate axes.

Further, "quiver3" can be used to plot these vectors and it's "LineSpec" can be used to set the color or the lines as you mentioned.

You can refer to the following documentation to know more about “quiver3” function:

https://www.mathworks.com/help/matlab/ref/quiver3.html

Hope this helps in solving your issue.