Question

Find an equation of the plane that contains all the points that are equidistant from the given points. (-10, 5, 2), (6, −2, 4). I know that to do this problem you need a normal vector to the plane and a point on the plane. The point on the plane is determined by the midpoint of the line segment connecting the two points. The normal vector is basically the vector connecting the two points a & b . My question is this...are we are assuming this line segment to be perpendicular to the plane ?Because couldn't you also argue that the line segment is intersecting the plane at an angle in which case the line segment is not normal and the point a & b could still be equidistant from all points on the plane? I am just trying to visualize this a little better in 3d. Thanks

          Find an equation of the plane that contains all the points that are equidistant from the given points.
(-10, 5, 2), (6, −2, 4). 

I know that to do this problem you need a normal vector to the plane and a point on the plane. The point on the plane is determined by the midpoint of the line segment connecting the two points. The normal vector is basically the vector connecting the two points a & b . 

My question is this...are we are assuming this line segment to be perpendicular to the plane ?Because couldn't you also argue that the line segment is intersecting the plane at an angle in which case the line segment is not normal and the point a & b could still be equidistant from all points on the plane? 

I am just trying to visualize this a little better in 3d. Thanks

Added by Tre A.

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