multivariable calculus problem...

[chen188]

Let M be the plane x+2y +z +1 = 0 and note that the point A(?2, 1,?1) lies
in M. Among all lines that lie entirely in the plane  and pass through the point A, find the
one that is the farthest possible to the point P(2, 3, 3).

I am woking on this homework but can hardly think of a way to solve it...
Could someone help me with this problem? A picture illustration is greatly appreciated!! Thank you!!!

 

[Deleted member 4993]

Let M be the plane x+2y +z +1 = 0 and note that the point A(?2, 1,?1) lies
in M. Among all lines that lie entirely in the plane  and pass through the point A, find the
one that is the farthest possible to the point P(2, 3, 3).

The line AP must be perpendicular to such a line.

I am woking on this homework but can hardly think of a way to solve it...
Could someone help me with this problem? A picture illustration is greatly appreciated!! Thank you!!!