a) Prove that (1,2,3), (4,5,6), and (0,4,2) are vertices of a right triangle in R3. b) Find

Question:

a) Prove that (1,2,3), (4,5,6), and (0,4,2) are vertices of a right triangle in R3.
b) Find all nonzero vectors orthogonal to (1,-1, 0) which lie in the plane z = x.
c) Find all nonzero vectors orthogonal to the vector (3, 2, -5) whose components sum to 4.