What is the angle between the lines with direction ratios $a, b, c$ and $b - c, c - a, a - b$, where $a, b, c$ are not all equal?

Explanation

1. 01

   $a(b - c) + b(c - a) + c(a - b) = ab - ac + bc - ab + ca - bc = 0$.

2. 02

   So $\cos \theta = 0$ and $\theta = \frac{\pi}{2}$, whatever $a, b, c$ are.