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A sheaf of planes with an axis, r, is a set of planes that contain the line r.

The equation of the sheaf of planes with axis, r, is:

Dividing by λ and making , the equation becomes:

Example

Find the equation of plane that passes through the point (3, 2, −3) and belongs to the sheaf of planes with its axis on the following line:

Parallel Sheaf of Planes

Two planes are parallel if the coefficients x, y, z are proportional to their equations but their independent terms are not.

All planes that are parallel to a given plane admit an equation in the form:

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Example

Find the equation of the plane that passes through the point (3, −1, 2) and is parallel to .

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.