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plane passing to the cuts

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Find an equation of the plane that passes through the point (1,2,3) and cuts off the smallest volume in the first octant.

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Solution Summary

The general equation of a plane passing to the cuts is depicted here.

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Problem:

Find an equation of the plane that passes through the point (1,2,3) and cuts off the smallest volume in the first octant.

Solution:

The general equation of a plane passing to the cuts (a, b, c) is
( 1)
If the plane passes trough the point (1,2,3), the above equation needs to by satisfied by the coordinates of this point:
( 2)
The volume of the body formed by this plane with ...

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