Area of a triangle in space using determinants from 3 points

Question

I know there is a way to find the area in plane using 3 points but when it comes to space(3D) does it work too? if so how should it look?

Thanks

You can see here: https://math.stackexchange.com/questions/427528/why-determinant-is-volume-of-parallelepiped-in-any-dimensions — Emilio Novati, Dec 24 '18 at 10:56

score 0 · Accepted Answer · answered Dec 24 '18 at 11:17

If you have three points $A,B,C$ you can form the vectors $AB$ and $AC$.

The norm of the cross product vector $AB\times AC$ is twice the area of the triangle $ABC$

Since the cross product is found be a determinant, the area of a triangle could also be found by a determinant.

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