Math Calculators, Lessons and Formulas

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« Line in three dimensions
Analytic geometry of three dimensions: (lesson 2 of 2)


Plane through Planes formula and perpendicular to the direction (a, b, c):

Planes formula

Example 1

Find the equation for the plane through the point (0, 1, 2) perpendicular to the vector (2, 1, -3).


Planes solution= (0, 1, 2)

(a, b, c) = (2, 1, -3)

The plane: 2 (x - 0) + 1 (y - 1) - 3 (z - 2) = 0

2x + y -3z = -5.

Plane through Planes, Planesand Planes:


Example 2:

Find the equation for the plane through the points (0, 1, 2), (2, 1, 3) and (3, 1, 0)


Planes example

Plane through Planes equationand parallel to the vectors Planes equationand Planes equation:

Planes equation

Plane through Plane formulaand Planes equation formulaand parallel to the direction (a,b,c):

Planes equation

The distance from the point distance from the pointto the plane ax+by+cz+d=0 is

distance from the point

The angle between two planes angle between two planes and analytic geometry is

angle between two planes

Two planes are parallel if their normal vectors are parallel (constant multiples of one another). It is easy to recognize parallel planes written in the form ax+by+cz=d since a quick comparison of the normal vectors n=<a,b,c> can be made.