Question

does anyone know how to prove a unit vector is orthogonal

Answer 1

rhat=(sin(theta)cos(rho),sin(theta)sin(rho),cos(theta)), thetahat=(-cos(theta)cos(rho),-cos(theta)sin(rho), sin(theta), and rhohat(sin(rho),-cos(rho), 0)

Answer 2

show that these unit vectors are orthogonal?

Answer 3

I am really not going to try to decipher what you wrote above, but two vectors are orthogonal if their dot product is zero

hope that helps!

Answer 4

PS: this is really a math question, so please post these things in the math group next time.
thanks

Answer 5

Thanks, It's directly from my physics homework though, but i think i can get it from that

Answer 6

yeah, I don't doubt that it came from your physics homework, but for the purposes of the site I think this qualifies as a math Q

see ya!

Answer 7

@TuringTest the question may be from mathematical tools of physics

Answer 8

As @TuringTest told you, the dot product does the trick.
You have to check all three combinations.

No wonder this question is in you physics book because these vectors are the unit vectors used in mechanics in spherical coordinates.

Answer 9

\[\hat r=\left(\sin \theta \cos \rho ,\sin\theta\sin \rho ,\cos \theta \right)\]\[ \hat \theta=\left(-\cos\theta\cos\rho,-\cos\theta\sin\rho,\sin\theta\right)\] and \(\hat \rho=\left(\sin\rho,-\cos\rho, 0\right)\)