In Solar thermal power plants with central receiver (https://en.wikipedia.org/wiki/Solar_power_tower) the mirrors (called heliostats) do not aim at the sun (vector 
) or the tower (vector 
), but the bisector of these two directions (vector 
):
) or the tower (vector ), but the bisector of these two directions (vector ):
The solar irradiance that bounces off the mirror is reduced by an amount proportional to reflectivity (assume 100% for this problem) and to the cosine of the angle between the normal vector to the heliostat and the other vector (sun or tower).
The aim of this problem is to calculate the value of the cosine of the angle (
) given the normalized vectors and that are known for every heliostat at every moment.
) given the normalized vectors and that are known for every heliostat at every moment.Hints:
- Vectors are 3×1, with norm = 1.
- Make use of scalar product to calculate cosines, taking advantage of the normalized vectors.
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It's so weird, but there is a difference in the result from using the law of cosines and the function arc cosine. And the error is significant, but I am glad the author has considered this.