Using vector method, show that the points `A(1,-1,0), B(4,-3,1)` and `C(2,-4,5)` are the vertices of a right -angled triangle.

Explanation

The position vectors of A,B,C are `(hati - hatj),(4hati - 3hatj + hatk)` and `(2hati - 4hatj + 5hatk)` respectively. Show that `vec(AB) + vec(BC) + vec(CA) = vec0` and `|vec(AB)|^(2) + |vec(BC)|^(2) = |vec(CA)|^(2)`.
`:. DeltaABC` is right angled at B.