Vector problem help wanted (I will use caps for vectors): If

I can't be bothered to do it formally, but I'll give you an idea. At least, that's how I'd solve it by intuition.
You're looking for the angle between aB+bA and aB+(-bA). aB and aB go in the same direction, so the angle is 0. bA and -bA go in opposite directions, so the angle is pi (180 degrees).
aB and bA are of the same length, both a*b.
This means they both influence the final angle in the same amount. So you just need the average of 0 and pi. Which is pi/2.

Hint: if the scalar product is 0 then the vectors are perpendicular (the angle between them is pi/2)

>>113041
Thanks this helped, for some reason I refused to think that aB and bA were definitely the same magnitude but as soon as I read it it clicked.

>>113046
That's mentioned in the notes so I figured that was going to be helpful but I wasn't sure how to use that without numerical values.

>>113029
Do you have a picture?

>>113029
>Answer is pi/2

Not true. Let a=<1,0> and b=<0,1> in (Z/2Z)^2, then C=<1,1> and D=<1,1> who's angle is 0.