[Math] How to calculate the area of a triangle ABC when given three position vectors $a, b$, and $ c$ in 3D

areatrianglesvectors

Where $a = ( 1, 2, 3), b = (2, 1, 3) $, and $c = (3,1,2). $

Best Answer

Heron works of course but it would be simpler to take half the length of the cross product $(b-a)\times(c-a)$.