Find the equation of the plane which passes through the points A(-1,-3,1), B(1,-2,0) and C(2,1,-1).

Calculate the shortest distance between the plane and the origin of the coordinate system.

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- Aug 20th 2008, 01:09 PMBogStandardEquation of plane.
Find the equation of the plane which passes through the points A(-1,-3,1), B(1,-2,0) and C(2,1,-1).

Calculate the shortest distance between the plane and the origin of the coordinate system. - Aug 20th 2008, 01:21 PMgalactus
Since A, B, and C lie in the plane, the vectors

and are parallel to the plane.

Therefore,

is normal to the plane, since it is perpendicular to .

By using the normal and the point (-1,-3,1) in the plane, we get the

point-normal form:

To find the distance between a point and a plane, use the formula: