I think you made an error with calculating the vector ##\vec{BC}=[-4,0,0]##. I think you missed the minus sign here. You also want to consider ##\vec{BA}## instead of ##\vec{AB}##, so your solution checks out because two negatives cancel each other out.
Perhaps I'm misunderstanding your convention but I use ##\vec{AB}= \vec{B}- \vec{A}##.