(717, #33) Find an equation of the plane that passes through the point ( 0, 1, 2 ) and contains the line
x = y = z.

Solution:

The points ( 0, 0, 0 ), ( 1, 1, 1) and ( 0, 1, 2 ) are on the plane.

Let a be the vector from ( 0, 0, 0 ) to ( 1, 1, 1 ); a = < 1, 1, 1 >

Let b be the vector from ( 0, 0, 0 ) to ( 0, 1, 2 ); b = < 0, 1, 2 >

The normal of the two vectors is:

The general equation of a plane is:

or

or

1x - 2 y + z = 0

by: nl