Fourth point given three coordinates

In summary, to find the fourth point S coordinate, one would need to know the coordinates of points P, Q, and R, the torsion angle between PQR and QRS, the bond length RS, and the bond angle QRS. Using equations A, the torsion angle can be calculated, but since there are three unknowns for point S, a numerical method such as Newton-Raphson or linear interpolation would need to be used to find the coordinates of point S.
  • #1
Dibyajyoti Das
1
0
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
 
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  • #2
.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.
 

FAQ: Fourth point given three coordinates

What is the concept of "Fourth point given three coordinates"?

The concept of "Fourth point given three coordinates" is a mathematical problem that involves finding the coordinates of a fourth point on a plane, given the coordinates of three other points. This problem is commonly encountered in geometry and navigation.

What is the formula for finding the fourth point given three coordinates?

The formula for finding the fourth point given three coordinates is based on the concept of midpoint. The coordinates of the fourth point can be calculated by finding the midpoint of two of the given points, and then finding the midpoint of the third point and the previously calculated midpoint.

How do I solve the "Fourth point given three coordinates" problem?

The "Fourth point given three coordinates" problem can be solved by following these steps:
1. Write down the coordinates of the given points in the form (x,y).
2. Use the formula for finding the midpoint of two points to calculate the midpoint of two of the given points.
3. Use the formula again to find the midpoint of the third point and the previously calculated midpoint.
4. The coordinates of this midpoint will be the coordinates of the fourth point.
Note: There are other methods of solving this problem, such as using the distance formula and slope formula.

What are some real-life applications of the "Fourth point given three coordinates" problem?

The "Fourth point given three coordinates" problem has a variety of real-life applications, including:
- Navigation: In order to find the coordinates of a destination, navigation systems use the coordinates of three known points (such as satellites) to calculate the coordinates of the fourth point (the destination).
- Surveying: Surveyors use this problem to determine the location of a point based on the coordinates of three other points.
- Engineering: In engineering, this problem can be used to determine the coordinates of a point on a structure, such as the location of a support beam.
- Geometry: This problem is commonly used in geometry to find the coordinates of a point on a line or a plane.

What are some tips for solving the "Fourth point given three coordinates" problem?

Here are some tips to keep in mind when solving the "Fourth point given three coordinates" problem:
- Double check the coordinates of the given points and make sure they are written in the correct order (x,y).
- Use the correct formula for finding the midpoint of two points, which is (x1+x2)/2 for the x-coordinate and (y1+y2)/2 for the y-coordinate.
- Use the same formula for finding the midpoint of the third point and the previously calculated midpoint.
- If you are using the distance formula or slope formula, make sure to use the correct values for x and y.
- Practice makes perfect! The more you solve this problem, the easier it will become.

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