Hello, I have a simple(or not?) math problem: I have equations of 3 lines in R3 trought the origin: line l1: |λ1*x+β1*y+γ1*z=0 |λ2*x+β2*y+γ2*z=0 line l2: |λ3*x+β2*y+γ3*z=0 |λ4*x+β3*y+γ4*z=0 line l3: |λ5*x+β4*y+γ5*z=0 |λ6*x+β5*y+γ6*z=0 I know every λ, β and γ - they are real constants. I also have a plane δ and : l1 intersects δ in point p1, l2 intersects δ in point p2, l3 intersects δ in point p3 I also know: ....the distance between p1 and p2 = h ....the distance between p2 and p3 = w ....p1, p2 and p3 form a right triangle with right angle at p2 (h2+w2=(p1p3)2) I want to find the equation of δ in terms of λ, β, γ, h and w _______________________________ it should be easy to find the equation of the plane if I find the points p1, p2 and p3 I think I should compose a system, containing: ....the first six equations(which are linear, so it should be easy to solve with matrices), ....the equation for right angle in R3: w2+h2=(p1p2)2, ....the two equations for distances w and h: h2=(p1x-p2x)2+(p1y-p2y)2+(p1z-p2z)2 and w2=(p2x-p3x)2+(p2y-p3y)2+(p2z-p3z)2 There are 9 equations with 9 unknowns (3 points, each with 3 coordinates) - it should be solvable. Have you got any ideas how to solve this? If there weren't 3 quadratic equations it would be easy. *I know that there should be 2 planes, matching the conditions - one that I've drawn(see the image) and the other is at the opposite side of the origin. I think the two roots of the quadratic equations should find them.