a × [(r - b) × a] + b × [(r - c) × b] + c × [(r - a) × c] = 0 ⇒ a . a (r - b) - (a . (r - b)) a + b . b (r - c) - (b . (r - c)) b + c . c (r - a) - (c . (r - a)) c = 0
⇒|a|2(r−b)−(r.a)a+|b|2(r−c)−(r.b)b+|c|2(r−a)−(r.c)c=0 [∵ a b, c are mutually perpendicular; ∴ a . b = b . c = c . a = 0]