Question

Calculus & Vectors help:
Triangle ABC has vertices A(1, 2, 3), B(4, 0, 5) and C(3, 6, 4). Show that ΔABC is a right triangle.

Step by step please and thank you. :)

Answer 1

first find AB,BC and CA
and check if the dot product of any two of them is 0

Answer 2

here AB =<3,-2,2> BC = <-1,6,-1> and CA =<2,4,1>
now dot product of AB and CA =3(2) +(4)(-2)+(1)(2) = 6-8+2 =0
hence triangle ABC is rt angled at A