Yes, you can do that,Ifthe given point is the origin (0, 0, 0). You don't say that. If the given point is then the function to be minimized is

Personally, I would NOT do it that way. Geometrically, the shortest distance from a point to a plane is along a line through the given pointperpendicularto the given line. That means it must lie in theplanecontaining the given point, perpendicular to the given line. Here, the given plane is x+ 2y+ 3z- 10= 0 so a perpendicular vector is given by <1, 2, 3> and the line through parallel to that vector, and so perpendicular to the plane, is , , . Determine the point where that line crosses the given plane and find the distance from that point to .

If the given point really is (0, 0, 0), the perpendicular line is given by x= t, y= 2t, z= 3t. Determine where that crosses the given plane by replacing x, y, and z in the equation of the plane by those: x+ 2y+ 3z- 10= t+ 2(2t)+ 3(3t)- 10= 14t- 10= 0. Solve that for t.