# Fourth point given three coordinates

1. Feb 6, 2014

### 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

Last edited: Feb 6, 2014