I'm absolutely exhausted working on this problem. I think I am very close, but I don't know what to do from here. I've tried a lot of different algebraic approaches.
So the problem says to prove A is perpendicular to B if |a-b| = |a+b|(we are talking about vectors and this is calculus class and this unit's recent lessons include the dot product and cross product).
What I've tried so far: I've tried drawing a diagram and using simple vector math and the property of a right triangle I noticed that if A and B are set up as connecting vectors at a right angle, then |a+b| would be the hypotenuse and |a-b| would be the hypotenuse of a mirrored right angle triangle. From there I tried plugging it into the Pythagorean formula as such:
C^2 = A^2 + B^2 since this would prove A and B are perpendicular Since C = |a+b| = |a-b| I substituted in...
|A+B||A-B| = |A|^2 + |B|^2
|A^2-B^2| = |A|^2 + |B|^2
I've been working on this for hours trying rearranging and I think I am need to try something new. I realize the dot product will prove perpendicular, but I don't know how to link the two. I'm stumped;
Any help is appreciated.