I have two unit vectors, say N and R which are perpendicular to each other. I want to find a third vector V which is also perpendicular to N but is rotated around it by a specified angle relative to R. I'm not sure how to work this out?
To help explain what I am doing: assume we have a perfectly spherical planet that is perfectly smooth (no geographical features). At a specified lat,long, I have a specified wind direction. 0° is a wind that blows due North, 90° blows due West, etc.
From these assumptions I can work out N (normal to the wind direction and normal to the ground) and R (in the plane that is tangent to the surface but facing due North).
How can I calculate V from these two vectors (in the same plane as R such that the angle from R to V is theta)? Or is there is an easier way to calculate this unit vector given latitude, longitude and wind direction? I want an answer in 3D space.