Solving Line-Plane Intersection: Tips and Guidance

[E=m(C)^2]

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.

 

[Galileo]

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.

 

[HallsofIvy]

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.

 

[Hootenanny]

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.

 

[Hootenanny]

Please don't double post E=mc².

 

[E=m(C)^2]

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.