- #1

kent davidge

- 933

- 56

I worked out similar problems in the early Calculus 2 classes (Now I'm doing Calculus 3). But I'm struggling to get it complete.

So what I've being doing:

##p## = point on the sphere of radius ##r##

##x## = general point on ##R^3##

##(x - p)## = first basis vector

##(x - p) \cdot p \stackrel{!}{=} 0##

##\Rightarrow x^1p^1 + x^2p^2 +x^3p^3 = r^2##

This should give the components of the first basis vector

For the second basis vector, I think, it's necessary that it be orthogonal to both the first and to ##p##. So

##(y - p) \cdot p \stackrel{!}{=} 0## and ##(y - p) \cdot (x - p) \stackrel{!}{=} 0##

I solved this a couple of times even using mathematica to make sure nothing's wrong, but it's just a matter of substitute into some values to see that this doesn't give right results.

What am I doing wrong?