simple geometry problem

Hi,

This is the situation: for a certain position on earth (p1) I have
calculated the xyz coordinates and I have constructed a plane (A1)
through that point and perpendicular to the earth radius going trough
it (this plane is how the observer perceives the earth's surface). I
then calculated the point where this plane intersects the earth axis
(a1). The vector from p1 to a1 (v1) is the north direction for an
observer in p1 (on the northern hemisphere of course). I now want to
calculate the vector in the plane A1 which has a certain angle (alpha1)
with v1. How can I do this?

Thanks
Piet

.

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