Find parametric question for the plane

In summary, the plane can be represented parametrically by using two parameters, x and y, or two distinct variables, u and w, with z being a function of x and y. Finding two independent vectors perpendicular to the normal of the plane can help determine the parametric equations.
  • #1
bonbon
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Homework Statement


Give parametric questions for the plane : 2x-3y+z-6=0


The Attempt at a Solution



i know that the normal is (2,-3,1)
how do i find the direction vector of the plane?
 
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  • #2
The plane has two linearly independent 'direction vectors'. Find any two independent vectors perpendicular to your normal.
 
  • #3
Dick is assuming that by 'direction vector', you mean two independent vectors in the plane. I've only seen the term used with lines.

I wonder if you are not confusing this with "find the parametric equations for a line". To do that you would find 'direction vector' for the line. Parametric equations for a plane will involve two parameters. Here, since you can write z as a function of x and y, z= 6- 2x+ 3y, you can use x and y themselves as parameters or, if you prefer distinct variables, x= u, y= w, z= 6- 2u+3w.
 
  • #4
That's a much more direct way. I was fixated on the 'direction vector' (basis) picture.
 

FAQ: Find parametric question for the plane

What is a parametric question for a plane?

A parametric question for a plane is a question that involves finding a specific set of equations (known as parametric equations) that describe the position and movement of a point on the plane. These equations typically involve a parameter, which represents a variable value that changes as the point moves.

How do you find the parametric equations for a plane?

To find the parametric equations for a plane, you first need to know the coordinates of two points on the plane. These points will serve as the starting and ending points for your parametric equations. Then, you can use these points to determine the values for the parameters in the equations.

Can parametric equations describe any point on a plane?

Yes, parametric equations can describe any point on a plane, as long as the equations are properly set up and the parameters are chosen within the appropriate range. These equations can also be used to describe the movement of a point on the plane over time.

What is the purpose of using parametric equations for a plane?

The purpose of using parametric equations for a plane is to describe the position and movement of a point on the plane in a more efficient and organized manner. These equations can also make it easier to visualize and understand the behavior of the point on the plane.

Are there any limitations to using parametric equations for a plane?

While parametric equations can be very useful for describing points on a plane, they do have some limitations. For example, they may not be able to accurately describe certain complex shapes or movements on the plane. Additionally, parametric equations may be more difficult to work with than other types of equations, such as Cartesian equations.

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