Trying to simplify code to see if 3 vectors are at right angle. Unsure of outcome.

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

Answer 1

[Alan Stevens]

The dot product is zero if the vectors are at right angles.

help dot

[Jessica]

dot - ok

but... it still does not give any zero...

P = [3 2 4]
Q = [5 0 2]
R = [6 4 5]
PQ2 = dot(P,Q)  % returns 23
QR2 = dot(Q,R)  % returns 40
RP2 = dot(R,P)  % returns 46

and there is a right angle, as is calculated by the longer code.

Answer 2

[Bruno Luong]

>> dot(Q-P,R-P)

ans =

     0

So PQ is right angle with PR, etc...