lets say that we have three points A(xa,ya,za), B(xb,yb,zv), C(xc,yc,zc) with known coordinates in 3d space. Is there a method to calculate the coordinates (x,y,z) of another point D for which the following applies:
1) the angle ABD is equal to DBC and with known value lets say θ
2) The |BD| is also known lets say l.
I need a method that can easily imported to a program language such as fortran like a 3x3 system that can be easily solved calling a subroutine from the available library.
Two equations come to my mind so far:
the firsts has to do with the inner product of the vectors
AB*BD=|AB|.|BD|.COSΘ
CB*BD=|CB|.|BD|.COSΘ
and
sqrt((x-xb)^2+(y-yb)^2+(z-zb)^2)=l
but the system so far is not linear and it will be difficult to input to a code.