# Finding the smallest angle between two vectors

I have two vectors: $A = i-3j+2k$ and $B = -3i+4j-k.$

I have already found the angle between the two to be ~$157.6$ degrees, but I am required to find the smallest angle between the two - I am not sure what that means exactly and can't seem to find the answer online. I would be glad if you could help me out with that.

They are position vectors in $\mathbb{R}^3$. Two vectors describe a plane so I presume you are being asked to find the angle between the two vectors in the plane they describe.
I've added a small illustration (done in Geogebra) to show what I mean. The two points $A$ and $B$ are described by the vectors you gave. The blue plane is described by $A, B$ and the origin and the angle between these two vectors is $153^{\circ}$ (not sure if the angle is properly visible). You can compute this angle via the dot product. If you used the dot product and got to $157.6^{\circ}$ there may be a rounding error of some description in your calculation. Either way, I believe this may be what your teacher is looking for. Does this help?