Is My Solution for 3D Triangle Area Correct?

[gneill]

If their dot product equals zero then they are perpendicular which my numbers seem to pass. As long as I'm doing the dot product right which I am pretty sure I am multiplying like values together and adding them.

Can you show that work?

 

[DODGEVIPER13]

A=AlphaUx+3Uy-2Uz and B=4Ux+betaUy+8Uz then by observation I noticed if I plugged 1 in for alpha then when I multiplied 4Ux and 1 Ux I would get 4. I then saw that is I plugged 4 in for beta then when 3Uy and 4Uy multiplied I would get 12. These added together gave me 16 and when -2Uz and 8Uz I get -16 when added together I get 0 which I assumed was right but I'm guessing its not.

 

[gneill]

A=AlphaUx+3Uy-2Uz and B=4Ux+betaUy+8Uz then by observation I noticed if I plugged 1 in for alpha then when I multiplied 4Ux and 1 Ux I would get 4. I then saw that is I plugged 4 in for beta then when 3Uy and 4Uy multiplied I would get 12. These added together gave me 16 and when -2Uz and 8Uz I get -16 when added together I get 0 which I assumed was right but I'm guessing its not.

Okay, previously you claimed $\alpha = 4$ and $\beta = 1$. Now you've swapped the values after checking. Always check!

While this (new) pair of values is one particular solution, you can get a general solution by expanding the [STRIKE]cross[/STRIKE] dot product symbolically and setting it to zero. You'll notice it yields one equation in two unknowns. What does that tell you?

Edit: Oops, I meant dot product, of course!

 

[DODGEVIPER13]

Ok I got something wonky trying to do the cross product of that I can't upload it until around 1 so ill do it then but typically when you have 2 unknowns I would need a second equation correct? They must then both multiply times the constants to form the 0 maybe?

 

[gneill]

Ok I got something wonky trying to do the cross product of that I can't upload it until around 1 so ill do it then but typically when you have 2 unknowns I would need a second equation correct? They must then both multiply times the constants to form the 0 maybe?

Check my edit of my previous post: I meant DOT product, not CROSS product, of course.

If a system of equations is underdetermined (more unknowns than equations), then you can have an infinite number of solutions but a fixed relationship between the variables...

 

[DODGEVIPER13]

ah makes sense so this obviously isn't the only solution but nonetheless one that will be correct right?

 

[gneill]

ah makes sense so this obviously isn't the only solution but nonetheless one that will be correct right?

Well, certainly not wrong, but at best incomplete