Solving Parametric Equations for the Equation of a Plane

In summary, the conversation discusses using parametric equations to solve for the equation of a plane and obtaining the normal vector to the plane from the coefficients of the equation. The final equation for the plane is x-2y+z=0, and it is noted that this can be used to easily determine the normal vector.
  • #1
Erenjaeger
141
6

Homework Statement


parametric equations are
x=s+2t
y=2s+3t
z=3s+4t

trying to solve for equation of the plane and then take the coefficients of the equation to get the vector normal to the plane

Homework Equations

The Attempt at a Solution



apparently t=2x-y
and s=2y-3x
and therefore the equation of the plane is x-2y+z=0
but for me solving the first equation for t just gives t=x-s/2
 
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  • #2
Erenjaeger said:

Homework Statement


parametric equations are
x=s+2t
y=2s+3t
z=3s+4t

trying to solve for equation of the plane and then take the coefficients of the equation to get the vector normal to the plane

Homework Equations

The Attempt at a Solution



apparently t=2x-y
and s=2y-3x
and therefore the equation of the plane is x-2y+z=0
but for me solving the first equation for t just gives t=x-s/2
From your equation of the plane, if it's correct, you can get a normal to the plane by inspection.
 

Related to Solving Parametric Equations for the Equation of a Plane

1. What are parametric equations?

Parametric equations are a set of equations used to express variables in terms of one or more parameters. They are often used to describe complex shapes or curves in mathematics and science.

2. How do you solve parametric equations for the equation of a plane?

To solve parametric equations for the equation of a plane, you need to first identify the parameters and variables in the equations. Then, you can use the equations to create a system of equations and solve for the variables using techniques such as substitution or elimination.

3. What is the importance of solving parametric equations for the equation of a plane?

Solving parametric equations for the equation of a plane allows us to understand and analyze the behavior of complex curves or shapes in three-dimensional space. It also helps us to make predictions and solve problems in fields such as engineering, physics, and computer graphics.

4. What are some common methods used to solve parametric equations for the equation of a plane?

Some common methods used to solve parametric equations for the equation of a plane include substitution, elimination, and graphing. Other advanced techniques such as vector methods and calculus can also be used depending on the complexity of the equations.

5. Can parametric equations be used to represent any shape or curve?

Yes, parametric equations can be used to represent any shape or curve in three-dimensional space. However, the complexity of the equations may vary depending on the shape or curve being represented.

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