June 26, 2019

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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