Finding Coordinates of Intersection in Parametric Forms

[TheFallen018]

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 :)

 

[mrtwhs]

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

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

 

[TheFallen018]

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

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

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

 

[mrtwhs]

\(\displaystyle x-5=t\), so \(\displaystyle x=\) ? Do the same for \(\displaystyle y\) and \(\displaystyle z\).