Posted by **alice** on Monday, March 16, 2009 at 6:30pm.

how do you find the coordinates of the point (x, y, z) on the plane z = 1 x + 1 y + 2 which is closest to the origin

- math -
**Reiny**, Monday, March 16, 2009 at 7:44pm
the closest point is surely on a line from (0,0,0) meeting the plane at right angles.

but the normal to the given plane is (1,1,-1)

so the line must have direction (1,1,-1)

it's parametric equations would be:

x = k

y = k

z = -k

sub that in to the plane to find the value of k, sub back in the parametrics

and voila, there is your point.

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