How to turn these symmetric equations into the general form?

In summary, the student tried to solve a problem using a method that wasn't the recommended way and was having trouble. The student was told that the problem wasn't solved using that method and was shown the correct way. The problem was solved using a different method that the student had forgotten.
  • #1
Regtic
75
3
I was solving this problem
ImageUploadedByPhysics Forums1418428585.222891.jpg


and I didn't want to do it the really long way by finding the equation of B(t) by first finding T(t) and N(t). So i took the cross product of r' and r'' so that they would be in the direction of B. Found the parametric equation of the plane but the book answer was in the general format.
ImageUploadedByPhysics Forums1418428883.823746.jpg


How do I turn this into the general format to check my answer? It should be 2X +Y +4Z -7 = 0

Whenever I try i just get two equations that don't mix to give me x y and z in one equation but it should be right.
 
Last edited:
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  • #2
Regtic said:
I was solving this problem View attachment 76531

and I didn't want to do it the really long way by finding the equation of B(t) by first finding T(t) and N(t). So i took the cross product of r' and r'' and took their cross product so that they would be in the direction of B. Found the parametric equation of the plane but the book answer was in the general format. View attachment 76532

How do I turn this into the general format to check my answer? It should be 2X +Y +4Z -7 = 0

Whenever I try i just get two equations that don't mix to give me x y and z in one equation but it should be right.

That's not the equation of a plane. It's the equation of a line. You might want to try the long way.
 
  • #3
Why can't you do it my way? I know it works, I've done it on other problems. My teacher's done it like that before too.
 
  • #4
Regtic said:
Why can't you do it my way? I know it works, I've done it on other problems. My teacher's done it like that before too.

I don't know what you are doing. Can you show us?
 
  • #5
Redid it to make it a bit clearer

ImageUploadedByPhysics Forums1418431044.682652.jpg
 
  • #6
I'm with Dick here. The symmetric equations you show in post #1 are for a line, not a plane.
 
  • #7
In your 2nd attachment, under "Normal Plane" you have (12, -16, -2)t (1, 1, 1). That can't be the equation of a plane, because (1) it's not an equation, and (2) there should be two parameters, not just one, in the parametric form of the equation of a plane.
 
  • #8
Mark44 said:
In your 2nd attachment, under "Normal Plane" you have (12, -16, -2)t (1, 1, 1). That can't be the equation of a plane, because (1) it's not an equation, and (2) there should be two parameters, not just one, in the parametric form of the equation of a plane.
Ooo right. Damn, I forgot a lot from linear. Literally not a plane with only 1 parameter. Ok thanks
 

Related to How to turn these symmetric equations into the general form?

What is the general form of a symmetric equation?

The general form of a symmetric equation is f(x) = ax + b, where a and b are constants. This form can be used to find the x-intercept and y-intercept of the equation.

How do I determine if an equation is symmetric?

An equation is symmetric if it remains unchanged when you swap the input and output variables. In other words, if f(x) = y, then f(y) = x. This is often represented as f(x) = f-1(x).

What are the steps to convert a symmetric equation to the general form?

To convert a symmetric equation to the general form, follow these steps:
1. Rewrite the equation as f(x) = y.
2. Replace x with f-1(y) to get f(f-1(y)) = y.
3. Use the definition of symmetry (f(x) = f-1(x)) to get f(y) = f-1(y).
4. Solve for y to get the general form f(y) = ay + b, where a and b are constants.

Can all symmetric equations be written in the general form?

No, not all symmetric equations can be written in the general form. Some equations may have a more complex form that cannot be simplified to the general form. However, many common symmetric equations, such as quadratic, cubic, and exponential functions, can be written in the general form.

What are the benefits of converting an equation to the general form?

Converting an equation to the general form can make it easier to identify important characteristics, such as the x- and y-intercepts, slope, and symmetry. It can also make it easier to graph and solve the equation, as the general form can be used to find points on the graph and to manipulate the equation algebraically.

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