Which Vectors Correctly Determine the Interior Angle at B in a 3D Parallelogram?

[ctg7w6]

Homework Statement

Parallelogram in 3d with vectors. Points: A(2,-1,4); B(1,0,-1); C(1,2,3); D(2,1,8)

I need the interior angle at B in degrees.

Homework Equations

cos(theta) = (Vector1 dot product vector2) / (magnitude of v1 * magnitude of v2)

The Attempt at a Solution

I used vectors BA and BC. I got 39 degrees. The answer sheet that I have uses AB and BC as the vectors and gets 140 degrees. Which vectors should I use? The picture in the homework makes the angle at B look like one of the smaller angles in the parallelogram, but I know you shouldn't trust pictures, because they might not be drawn to scale.

So, I know how to do the problem, I just don't know which vectors are the correct ones to use. Could someone also explain WHY the particular set of vectors should be used instead of the other set? Thank you very much!

 

[Dick]

You did it right. The book did it wrong.

 

[ctg7w6]

Thank you! That problem has been eating at me for the past few days and driving me nuts!