I need to find the point in the plane x + 2y + 3z = 6 that is nearest the origin.
So the parametric equations of the line passing through the origin and in the direction of this normal vector will be:
x = at
y = bt
z = ct
The point where this line cuts the plane will be the point that's closest to the origin:
.
Therefore the coordinates of the point in the plane closest to the origin are:
.
.
.
And as a bonus, the answer to what the closest distance is equal to is ..........