Sure. I don't mind. I might not know the answer, but I'm certainly willing to give it a go.
Awesome, thanks dude!
So a week ago I messaged my teacher asking something simple but I am still left confused. This has to do with creating a scalar equation.
For example; determine the scalar equation of P(1,0,4) Q(3,1,-6) and R(-2,3,5). Usually you have to subtract one another to create points for the cross multiplication right. However doing them in different order yields different answers and my teacher said that it should be okay.
His words ''Yes, absolutely, the order doesn't matter. It yields the same answer regardless. If you were to do AB and AC, it would yield the same answer as AB and BC. Give it a try to see how it works.''
So for example PQ=Q-P=(3,1,6)-(1,0,4)=3-1,1-0,6-4=(2,1,2)
PR=R-P=(-2,3,5)-(1,0,4)=2-1,3-0,5-4=(1,3,1)
Cross multiply (PQxPR)= (1)(1)-(2)(3),(2)(1)-(2)(1),(2)(3)-(1)(1)=1-6,2-2,6-1=-5,0,5
Now if we did this for PQ and QR it would be like this;
PQ=(2,1,2)
QR=R-Q=(-2,3,5)-(3,1,-6)=-2-3,3-1,5+6=-5,2,11
Cross multiply them together (PQxQR)=(2)(2)-(11)(1),(11)(2)-(-5)(2),(-5)(1)-(2)(2)=-7,32,-9
I rushed this so if the answers are incorrect I apologize. So I've noticed that when I Add subtract the points in another order I get another answer.