I would like to calculate the following:
There are 3 points in space of which the coordinates are known: $C(a,b,c), M(d,e,f), A(g,h,i)$
Each point is a starting point of a line with a certain length. These lengths are known: $|CB|=l1,\, |MB|=l2,\, |AB|=l3$
There exist 2 possible points (B1 and B2) in space where the end points of these lines coincide. So what I would like to calculate are the coordinates of these 2 points.
The set of equations looks like this: $$(a-x)²+(b-y)²+(c-z)² = l1^2\\ (d-x)²+(e-y)²+(f-z)² = l2^2\\ (g-x)²+(h-y)²+(i-z)² = l3^2$$
B(x,y,z) = ?
Thank you in advance for any hint to solve this problem