you've understood that a, b, c form a triangle, so this means a, b, c vectors are on the same plane.

now, you know when we take a cross product of two non linear vectors, it will geometrically give the area of the parallelogram they make. also the half of that value would give the area of the triangle they make. so, axb, bxc and cxa refers to the same triangle so the moduls value of all three should be equal and since a,b,c are on the same plane, the direction of those cross products also should be the same which make those cross products equal