First off, sorry if this is in the wrong section. I was unsure of where to put it, and if there's a more suitable location please point me to it and I'll ask a mod to move it. Anyways, this appeared on my exam today, and I couldn't figure it out on the exam nor could the people that I spoke to.
a and b are unit vectors.
If a dotted with b = -1, show that a = -b
Also, it did not mention any dimension so the "brute force" method (solving for the general case <x,y,z> and <a,b,c> using the dot product definition) isn't ideal. Also, we were to find a method other than using the = |a||b|cos o formula.
I found a way to prove the opposite, as a vector dotted with itself is simply the length of the vector squared, in this case simply one, so if a = -b then a dotted b = a dotted -a = - (a dotted a) = -1. However, I couldn't find a way to link this logic in the other direction.