Finding Coordinates of Intersection in Parametric Forms

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SUMMARY

This discussion focuses on finding coordinates of intersection in parametric forms, specifically using the equations $$x-5=y-3=\dfrac{z}{2}=t$$ and the plane equation $$2x-2y+2z=D$$. Participants emphasize the importance of understanding parametric equations and the relationship between parallel planes, which share the same attitude numbers. The conversation highlights the need to derive the parameter $$t$$ from the plane equation and to calculate the constant $$D$$ using a given point.

PREREQUISITES
  • Understanding of parametric equations
  • Knowledge of plane equations in three-dimensional space
  • Familiarity with the concept of attitude numbers
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the derivation of parameters from parametric equations
  • Learn about the properties of parallel planes in 3D geometry
  • Explore methods for solving systems of equations involving parametric forms
  • Practice finding intersections of lines and planes using specific examples
USEFUL FOR

Students and educators in mathematics, particularly those focusing on geometry and algebra, as well as anyone looking to enhance their understanding of parametric forms and their applications in three-dimensional space.

TheFallen018
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Hey,

I have a couple of questions I've been doing online which have left me a little puzzled. The first one, I'm not really sure how to go about. I think a lot of that comes down to having not had a lot of experience with parametric forms.

I'll just post screenshots of where I'm up to on them, as they'll probably explain better where I'm up to.This is the one I'm having the most trouble with
View attachment 8080

This one, I've got most of the questions, but the last one is leaving me a little confused.

View attachment 8081

Any help would be amazing. Thanks :)
 

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$$x-5=y-3=\dfrac{z}{2}=t$$. Use the equation of the plane to get $$t$$.

Parallel planes have the same attitude numbers. So $$2x-2y+2z=D$$. Use the point to get $$D$$.
 
mrtwhs said:
$$x-5=y-3=\dfrac{z}{2}=t$$. Use the equation of the plane to get $$t$$.

Parallel planes have the same attitude numbers. So $$2x-2y+2z=D$$. Use the point to get $$D$$.

Hey man, I appreciate the help. I guess I'm still not very familiar with this sort of stuff. Would you be able to expand on that a little? Cheers
 
$$x-5=t$$, so $$x=$$ ? Do the same for $$y$$ and $$z$$.
 

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