Sorry, this is not a homework service. You can ask for hints and ideas, but not complete solutions.

Prove that for some combination of + and -, ± v ± b ± n = 0.

You can find out if the angle between two vectors is acute, right or obtuse by taking the dot product of the vectors. You have to be careful with orientation, though. For example, for the following vectors:

the dot product is negative even though the angle is acute. That's because when the vectors are drawn having the same starting point, the angle between them is obtuse.