Question

Prove the the triangle with vertices a(−2,4,0), b(1,2,−1) and c(−1,1,2) is regular.

Answer 1

See the offered decision:
one way is to calculate (and compare) lengths of AB, AC and BC:
AB²=(-2-1)²+(4-2)²+(0+1)²=14;
AC²=(-2+1)²+(4-1)²+(0-2)²=14;
BC²=(-1-1)²+(1-2)²+(2+1)²=14.
AB=AC=BC ⇒ the triangle is regular.