Given a triangle ABC, on which side of the triangle does the point D lie?

[VladStoyanoff]

So I've got the following problem:

I have points A, B, and C which form a triangle in a 3D space (each point of the triangle has x,y, and z coordinates). I need to find out on which side of the triangle point D lies. I do not have access to the normal of the triangle.

How am I supposed to solve this problem?

 

[fresh_42]

If you have the nine coordinates, then you have the plane and therewith the normal. If not, what do you have?

 

[VladStoyanoff]

If you have the nine coordinates, then you have the plane and therewith the normal. If not, what do you have?

I am not given any coordinates for the problem, actually, I am asking what kind of information I need so that I can solve the problem. Like a general way of solving it if that makes sense. After I have the normal how would I approach the question?

 

[fresh_42]

By the right-hand rule or something. In order to determine a side you must first have criteria to distinguish them. Two vectors spanning the plane, plus the normal give you either the right or left hand.

 

[FactChecker]

The coordinates of the four points, $A, B, C, D$, is all the information you need. You first must define which "side" is which.
Suppose you define the side by the cross product between the $V_1 = \bar{AB}$ and $V_2 = \bar{AC}$ vectors. Using the right-hand rule, form the cross product $N=V_1 \times V_2$. One side would be those points, $X$, where the vector from $A$ to $X$ has a positive dot product with $N$. The other side would have a negative dot product with $N$.

 

[Vanadium 50]

If you have the nine coordinates, then you have the plane

And three lines. Plug and check.

I am not given any coordinates for the problem

What then does it mean to say you have three points? What do you have about them if not their location?

 

[.Scott]

There are two ways of interpreting "side of the triangle".
One is which side of the triangles plane does point D land.
The other is which of the three sides of the triangle does point D land.

Go with @FactChecker for the first interpretation.

Else, I would start with vectors AD, BD, and CD.
What will their various cross products be?