Fourth point given three coordinates

[Dibyajyoti Das]

1.Hi,
Need to find fourth point S coordinate, given the below:
1. coordinates of P,Q,R,
2. torsion angle between PQR and QRS,
3. the bond length RS and
4. bond angle QRS.

Can anybody give me the way out?
2. Equaltions for Torsion angles
b1=PQ
b2=QR
b3=RS
where PQ,QR and RS are all vectors,
n1=⟨b1×b2⟩ and n2=⟨b2×b3⟩
ϕ=cos⁻¹(n1.n2 /(∥n| ∥m∥)...(eqn A)


3. The torson angle can be found easily given four points. However since there are three unknowns x,y,z of point S, its not possible here

 

[Asim Riaz]

.You can solve this problem using a numerical method like Newton-Raphson or linear interpolation.1. First find the cartesian coordinates of points P,Q and R2. Then calculate the bond length RS using distance formula3. Now calculate the bond angle QRS using the dot product formula4. Finally use the equations A to calculate the torsion angle between PQR and QRS5. Now set up two equations with three unknowns x,y,z for point S.6. Solve the equations using either Newton-Raphson or linear interpolation to get the coordinates of point S.