# Thread: Distance from a Plane

1. ## Distance from a Plane

Hi all, I'm having a bit of trouble with this linear algebra question, and would really appreciate some help:

Find the distance from P(3,0,-1) to the plane P described by the equation 4x + 2y -z = 6.
Find the closest point to P which lies on the Plane P.

I've got the distance -- that's (the square root of 21)/3.
But I keep getting the coordinates of the closest point wrong.
I get (4/3, 2/3, -1/3), but the answer's apparently (5/3, -2/3, -2/3)

What am I doing wrong?

2. Originally Posted by rorosingsong
Find the distance from P(3,0,-1) to the plane P described by the equation 4x + 2y -z = 6.
Find the closest point to P which lies on the Plane P.
If $\mathif{N}$ is the normal to the plane the find where the line $\mathif{P}+t\mathif{N}$ intersects the plane.