Distance from a point to a plane

[Sewoon]

I am trying to show that the point in the plane ax+by+cz=d closest to the origin is
P(ad/D^2, bd/D^2, cd/D^2) where D^2=a^2 + b^2 + c^2. How do I approach this? I tried using partial derivatives but got too complex after a while. Thanks

 

[mathman]

The vector (a,b,c) is perpendicular to the plane. Therefore the line given by parametric form (at,bt,ct) passes through the origin and intersects the plane at the point closest to the origin. Simply calculate the distance after finding t.