Area of a triangle in space using determinants from 3 points

areasolid-geometry

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

Best Answer

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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