Solving Line-Plane Intersection: Tips and Guidance

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Homework Help Overview

The discussion revolves around finding the coordinates of the intersection point between a given line and a plane. The line is represented in vector form, and the plane is defined by a linear equation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss substituting the parametric equations of the line into the plane's equation to find the value of the parameter t. There is also a focus on ensuring that the intersection point satisfies both the line and the plane equations.

Discussion Status

Some participants have offered hints and guidance on how to approach the problem, emphasizing the need to show personal effort in the discussion. Multiple interpretations of the problem setup are being explored, and there is an acknowledgment of the forum's rules regarding participation.

Contextual Notes

One participant notes the importance of demonstrating personal effort in order to receive assistance, in line with the forum's guidelines.

E=m(C)^2
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Help!

Hi everyone,
This is my very first post on physics forum! I was wondering if anyone could help explain to me how to find the coordinates of a point where a line intersects a plane.
The question I'm trying to do has given the line as r= (2, 7, -5) + t(1, 2, -1) and the plane as 2x + 3y - z=3.
Any advice or help would be much appreciated, thank you.
 
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The x,y and z coordinates of the points on the line are (2+t, 7+2t, -5-t) right?
Now those coordinates have to satisfy 2x+3y-z=3 to be in the plane. Just plug it in and see for what value it t they are.
 
E=m(C)^2 said:
Hi everyone,
This is my very first post on physics forum! I was wondering if anyone could help explain to me how to find the coordinates of a point where a line intersects a plane.
The question I'm trying to do has given the line as r= (2, 7, -5) + t(1, 2, -1) and the plane as 2x + 3y - z=3.
Any advice or help would be much appreciated, thank you.

Saying the line is given by the vector equation r= (2,7,-5)+ t(1, 2, -1) is the same as saying it is given by the parametric equations x= 2+ t, y= 7+ 2t, z= -5- t. Replace x, y, z in the equation of the plane to get an equation for t and solve.
 
Hi there E=mc2 and welcome to PF,

According to the rules of this forum, you must show some of your own efforts in order to gain assistance. However, if I may offer you the hint that any point of intersection must satisfy the equation of both the line and plane.

Edit: Halls beat me to it; I must learn to type faster. :smile:
 
Please don't double post E=mc2.
 
Thanks a lot guys, i really appreciate it. Sorry about the double post Hootenanny and believe me i made some effort but yeah didn't really show it, sorry about that. Won't happen again.
Thank you again.
 

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