# Solving Parametric Equations for the Equation of a Plane

• Erenjaeger
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.
Erenjaeger

## 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

## 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

Last edited by a moderator:
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

## 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.

## 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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