Spherical coordinates position vector

[mickry]

can anyone help me with this question:
A sphere of unit radius is centered at the origin. points U,V & W on the surface of the sphere have vectors u,v & w. find the position vector of points P&Q on a diameter perp to the plane containing points U,V & W?

can anyone help

 

[Astronuc]

In Cartesian coordinates if the points U, V, W are coplanar, to which position vectors u, v, w point, respectively, what can one do to create two planar vectors? Hint. What is the formula for the vector pointing from U to V? Similarly for V to W or U to W.

Now with two coplanar vectors, how does one find a vector perpendicular to those two?

 

[mickry]

tripple scaler product?