Problem with finding angle using dot products

[potetochippu]

Homework Statement

Find the cosines of the internal angles of the triangle which has the following coordinate vectors as its vertices: A(4,0,2) B(6,2,1) C(5,1,6)

Homework Equations

I understand that you have to find the 3 vectors which represents each side of the triangle in order to get the cosine.

My problem is, which vectors do I use for each angle? Let's say that I want to find the cosine of the angle at vertex B. Do I use vector AB and BC or do I use BA and BC? When I use AB(b-a=(2,2,-1)) and BC(c-b=(-1,-1,5)) the dot product of the vectors are negative whereas when I use BA and BC its positive hence I get different answers. Which one do I use and why?

 

[Curious3141]

You should order the dot product so that the same vertex comes at the start or end of both vectors. So either AB.AC or BA.CA is OK to find the cosine of the angle at vertex A. To avoid confusion, I'd say just stick with the first "rule" (make sure the first letters are the same).

This will give you a positive value if the internal angle is acute, and a negative value if the internal angle is obtuse.