Thread: Determining whether 4 points are coplanar. Answer check

The question asks, whether the points are (1,0,-1) , (0,2,3) and (-2,1,1) and (4,2,3) are coplanar.

I let (1,0,-1) be point A
let (0,2,3) point B
let (-2,1,1) point C
let (4,2,3) point D

So vector AB, AC, AD are


than using the triple scalar product



Considering that the triple scalar product is zero, would mean that the points are coplanar, correct?

But the answer is given as though that are not coplanar

Originally Posted by Craka

The question asks, whether the points are (1,0,-1) , (0,2,3) and (-2,1,1) and (4,2,3) are coplanar.

I let (1,0,-1) be point A
let (0,2,3) point B
let (-2,1,1) point C
let (4,2,3) point D

So vector AB, AC, AD are


than using the triple scalar product



Considering that the triple scalar product is zero, would mean that the points are coplanar, correct?

But the answer is given as though that are not coplanar

I'd just find the equation of the plane that three of the points lie in. Then test whether the fourth point satisfies the equation.

Originally Posted by Craka

The question asks, whether the points are (1,0,-1) , (0,2,3) and (-2,1,1) and (4,2,3) are coplanar.

I let (1,0,-1) be point A
let (0,2,3) point B
let (-2,1,1) point C
let (4,2,3) point D

So vector AB, AC, AD are


than using the triple scalar product



Considering that the triple scalar product is zero, would mean that the points are coplanar, correct?

But the answer is given as though that are not coplanar

I did the same computation as you (i.e. check if are linearly dependent by computing the determinant), and I confirm the points are coplanar.