MHB Finding Coordinates of Intersection in Parametric Forms

AI Thread Summary
The discussion revolves around finding the coordinates of intersection in parametric forms, with a focus on understanding the equations involved. The user expresses confusion regarding the application of parametric equations and how to derive values from them. Key points include the use of the equation of a plane to determine the parameter \( t \) and the concept that parallel planes share the same coefficients. The conversation highlights the need for clarification on how to manipulate the equations to solve for \( x \), \( y \), and \( z \). Overall, the user seeks guidance to enhance their understanding of these mathematical concepts.
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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