Calculate the normal vector between two nodes in the space

Hi! I have two nodes A and B. These are positioned in space with the same value of X and Y but different Z. The normal in this case would be n=[0 0 1] (red plane parallel to the XY plane).

I would like to calculate the normal n 'green' in the case of nodes A and C. Is this possible?

A = [-33.24 -10.70 7.41];
B = [A(1,1), A(1,2), A(1,3)+5];
N = [A;B];

C = [A(1,1), A(1,2)+7, A(1,3)+5];
NN = [A;C];

figure
plot3(A(1,1),A(1,2),A(1,3),'k.','Markersize',30);
hold on
plot3(B(1,1),B(1,2),B(1,3),'r.','Markersize',30);
plot3(C(1,1),C(1,2),C(1,3),'g.','Markersize',30);
plot3(N(:,1),N(:,2),N(:,3),'-k','LineWidth',1);
plot3(NN(:,1),NN(:,2),NN(:,3),'-k','LineWidth',1);
hold off
axis equal

(YZ view)

Answer 1

[Torsten]

n = [0 0 1] points from A to B. So I don't understand what you mean by "normal" to the line connecting two points in 3d.

Usually, it's the set of all vectors perpendicular to the line. You get a basis for this set of vectors by the "null" command:

A = [0 0 0];
B = [0 0 1];
AB = -A + B;
N = null(AB)  

N = 3x2

0 -1 1 0 0 0

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N.'*AB.'  % Check for orthogonality

ans = 2x1

0 0

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[Alberto Acri]

My terminology may not be correct.

The vector 'n' I called 'normal' because if I create a plane with the components of 'n' it turns out to be a plane parallel to the XY plane (because only Z varies). The value of 'n' is valid for all nodes from A to B.

I wanted to know if there was a way to identify the value of 'n' in case the direction of the nodes is AC. This value of 'n' will be the same for all nodes present between A and C (as for the AB case).

Let me know if I have made myself clear!

[Torsten]

Then, as in your first simple example, n is simply the vector connecting A and C, computed as -A+C ( maybe normalized to length 1 as (-A+C)/norm(-A+C) )