# Homework Help: Lines And Planes Query

1. Sep 3, 2006

### 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.

Last edited: Sep 3, 2006
2. Sep 3, 2006

### 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.

3. Sep 3, 2006

### HallsofIvy

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.

4. Sep 3, 2006

### Hootenanny

Staff Emeritus
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.

5. Sep 3, 2006

### Hootenanny

Staff Emeritus