Trying to simplify code to see if 3 vectors are at right angle. Unsure of outcome.
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I have an older code, which is rather long, and just to see if any angle is degrees, seems unnecessary, so I have tried to use "cross", but is is unsure of the output.
The vectors are at right angle, when I rotate the plot.
Old code:
P = [3 2 4]
Q = [5 0 2]
R = [6 4 5]
% distance between points √((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
sides = @(x1, x2, y1, y2, z1, z2) sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
PQ = sides(P(1), Q(1), P(2), Q(2), P(3), Q(3))
QR = sides(Q(1), R(1), Q(2), R(2), Q(3), R(3))
RP = sides(R(1), P(1), R(2), P(2), R(3), P(3))
Ra = rat(RP)
Rb = rat(QR)
Rc = rat(PQ)
% angle a^2 + b^2 = c^2 * 180/pi
angle = @(x1, x2, x3)(180/pi) * acos(-(x1^2-(x2^2+x3^2))/(2*x2*x3))
AngleA = angle(RP,QR,PQ)
AngleB = angle(QR,PQ,RP)
AngleC = angle(PQ,QR,RP)
% plot
x = [P(1) Q(1) R(1) P(1)]
y = [P(2) Q(2) R(2) P(2)]
z = [P(3) Q(3) R(3) P(3)]
xmax = max(x)
xmin = min(x)
ymax = max(y)
ymin = min(y)
zmax = max(z)
zmin = min(z)
figure('defaultAxesFontSize',18)
plot3(x,y,z)
the new code:
P = [3 2 4]
Q = [5 0 2]
R = [6 4 5]
PQ2 = cross(P,Q)
QR2 = cross(Q,R)
RP2 = cross(R,P)
Running the new shows that one element is 0, with the other 8 not.
Math says if the cross-product is = 0, then the angle is right.
Is this single Zero a sign of the 90-degree angle? Feels so insignificant (pun not intended).
Jessica
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