Finding a point on a line closest to another point

[Bugsy23]

I've got a point P=(-2,1,-2) and a line x+y-2z=0 and I need to find the point on the line that is closest to P. I've used the distance formula to find the shortest distance from P to the line, and I got the answer 3/√6, but I'm not sure that really helps me here. I can't seem to find anything that shows how to find the actual coordinates of the point on the line. Any help would be greatly appreciated. Thanks!

 

[stapel]

I've got a point P=(-2,1,-2) and a line x+y-2z=0 and I need to find the point on the line that is closest to P. I've used the distance formula to find the shortest distance from P to the line, and I got the answer 3/√6, but I'm not sure that really helps me here. I can't seem to find anything that shows how to find the actual coordinates of the point on the line. Any help would be greatly appreciated. Thanks!

The closest point will be on a line perpendicular to the given line; it'll be the intersection of that perpendicular line and the original line. Does that help?