Where Does a Line Meet a Plane?

[megr_ftw]

Homework Statement

Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = -1

Homework Equations

The Attempt at a Solution

vector of line= <1,2,-3>

Am I suppose to find the projection of the two vectors?

 

[Gregg]

Don't you need to find the values of t for which x+y-z=-1?

Plug x,y and z into the planes equation in terms of t, find the value of t for which the equality holds then transfer it back to the line to find the position of the intersection.

 

[megr_ftw]

plug -1 into the line equation right? and that should give me the value of t?

 

[Gregg]

I havn't done this for a while, but it looks like x+y-z=-1 means that (1+t) + 2t - (-3t) = -1 should give you t, and then you can work out the co-ordinates of this point.

 

[megr_ftw]

thanks I figured it out. intersects at point (2/3, -2/3, 1)