Solving Calc III Plane Equation with y=1, z=2

  • Thread starter Teachme
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    Calc iii
In summary, to find an equation for the plane containing the line y=1 in the xy-plane and z=2 in the xz-plane, you can use the formula Ax+By+Cz = 1, where z = 2-2y. This will give you the equation of the plane containing both lines.
  • #1
Teachme
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Homework Statement


Find an equation for the plane containing the line in the xy-plane where y = 1, and the line in the xz-plane where z = 2


Homework Equations


Ax+By+C= f(x,y) or (z)


The Attempt at a Solution


Ok so i started off by graphing and i see when x and y are 0 z = 2 and when z and x are x
y = 1
So i know that to find the slope n (Δz/Δy) = 2/1 = 2

After this I am lost as what to do. I use cramster, but the explanation is poor and
says Ax+By+Cz = 1, but I don't see how this equation is related.
 
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  • #2
Teachme said:

Homework Statement


Find an equation for the plane containing the line in the xy-plane where y = 1, and the line in the xz-plane where z = 2

Homework Equations


Ax+By+C= f(x,y) or (z)

The Attempt at a Solution


Ok so i started off by graphing and i see when x and y are 0 z = 2 and when z and x are x
y = 1
So i know that to find the slope n (Δz/Δy) = 2/1 = 2

After this I am lost as what to do. I use cramster, but the explanation is poor and
says Ax+By+Cz = 1, but I don't see how this equation is related.
What line in the yz-plane is is also in the plane whose equation you are looking for?
 
  • #3
z = 2 -2y?
 
  • #4
Teachme said:
z = 2 -2y?
Correct !
 
  • #5
Thanks for the help. Much appreciated. This one was bothering me for a while.
 

1. What is Calc III?

Calc III, short for Calculus III, is a college-level math course that focuses on the study of multivariable calculus. It builds upon the concepts learned in Calculus I and II, but extends them to functions in three-dimensional space.

2. What is a plane equation?

A plane equation is an equation that describes a flat, two-dimensional surface in three-dimensional space. It is typically written in the form ax + by + cz + d = 0, where a, b, and c are coefficients that determine the orientation of the plane, and d is a constant.

3. How do I solve a plane equation with y=1 and z=2?

To solve a plane equation with y=1 and z=2, you first need to substitute these values into the equation. This will leave you with an equation in terms of x, which you can then solve for. For example, if the equation is 2x + y + z = 5, and y=1 and z=2, then the equation becomes 2x + 1 + 2 = 5. Solving for x, we get x = 1.

4. What does y=1 and z=2 represent in a plane equation?

In a plane equation, y=1 and z=2 represent two specific points that lie on the plane. These points are used to help determine the orientation and position of the plane in three-dimensional space.

5. Why is it important to be able to solve plane equations?

Being able to solve plane equations is important for understanding and working with functions in three-dimensional space. It allows us to model and analyze real-world situations, such as the motion of objects in space or the shape of a surface. Additionally, it is a fundamental skill in many fields, including engineering, physics, and computer graphics.

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