OEF orthogonal distance --- Introduction ---

This module gathers actually 37 exercises on euclidean geometry of lines and planes: parallel, orthogonal, distance, orthogonal projection, etc.

Distance 2D by equation

In , compute the distance between the point and the line defined by the equation

.

Distance 2D parametric

In , compute the distance between the point and the line defined by the parametric system

, .

Distance 2D by points

In , compute the distance between the point and the line determined by the points

and .

Distance between two lines I*

Compute the distance in between the line defined by the parametric system

, , passing through the points

and

and the line defined by the parametric system

, , passing through the points

and .

Distance between two lines II*

Compute the distance in between the line defined by the parametric system

, , passing through the points

and

and the line defined by the parametric system

, , passing through the points

and .

Distance between two lines III*

Compute the distance in between the line defined by the parametric system

, , passing through the points

and

and the line defined by the parametric system

, , passing through the points

and .

Distance 3D - plane by equation

In , compute the distance between the point and the plane defined by the equation

.

Distance 3D - line by equation

In , compute the distance between the point and the line defined by the system



Distance 3D - line parametric

In , compute the distance between the point and the line defined by the parametric system

, , .

Distance 3D - line by points

In , compute the distance between the point and the line determined by the points

and .

Distance 3D - plane parametric

In , compute the distance between the point and the plane defined by the parametric system

, , .

Distance 3D - plane by points

In , compute the distance between the point and the plane determined by the points

, and .

Parallel lines 2D

What is the distance between the following two parallel lines in  ?

and
   

Parallel planes 3D

What is the distance between the following two parallel planes in  ?

and
   

Parallel lines 3D

What is the distance between the following two parallel lines in  ?

, , and

, ,    


Orthogonal 2D by equation

Find an equation of the line in passing through the point and orthogonal to the line defined by the equation

.

Orthogonal 2D parametric

Find an equation of the line in passing through the point and orthogonal to the line defined by the parametric system

, .

Orthogonal 2D by points

Find an equation of the line in passing through the point and orthogonal to the line determined by the points

and .

Orthogonal 3D by equation

Find an equation of the plane in passing through the point and orthogonal to the line defined by the system



Orthogonal 3D parametric

Find an equation of the plane in passing through the point and orthogonal to the line defined by the parametric system

, , .

Orthogonal 3D by points

Find an equation of the plane in passing through the point and orthogonal to the line determined by the points

and .

Parallel 2D by equation

Find an equation de the line in passing through the point and is parallel to the line defined by the equation

.

Parallel 2D parametric

Find an equation de the line in passing through the point and is parallel to the line defined by the parametric system

, .

Parallel 2D by points

Find an equation de the line in passing through the point and is parallel to the line determined by the points

and .

Parallel 3D - plane by equation

Find an equation of the plane in passing through the point and parallel to the plane defined by the equation

.

Parallel 3D - plane parametric

Find an equation of the plane in passing through the point and parallel to the plane defined by the parametric system

, .

Parallel 3D - plane by points

Find an equation of the plane in passing through the point and parallel to the plane determined by the points

, and .

Parallel parametric 3D

We have a line in defined by the following parametric system

, , .

For what value of the parameter the following plane is parallel to  ?


Projection 2D by equation

In , compute the orthogonal projection of the point on the line defined by the equation

.

Reply: the projection is ( , ).


Projection 2D parametric

In , compute the orthogonal projection of the point on the line defined by the parametric system

, .

Reply: the projection is ( , ).


Projection 2D by points

In , compute the orthogonal projection of the point on the line determined by the points

and .

Reply: the projection is ( , ).


Projection 3D - plane by equation

In , compute the orthogonal projection of the point on the plane defined by the equation

.

Reply: the projection is ( , , ).


Projection 3D - line by equation

In , compute the orthogonal projection of the point on the line defined by the system


Reply: the projection is ( , , ).


Projection 3D - line parametric

In , compute the orthogonal projection of the point on the line defined by the parametric system

, , .

Reply: the projection is ( , , ).


Projection 3D - line by points

In , compute the orthogonal projection of the point on the line determined by the points

and .

Reply: the projection is ( , , ).


Projection 3D - plane parametric

In , compute the orthogonal projection of the point on the plane defined by the parametric system

, .

Reply: the projection is ( , , ).


Projection 3D - plane by points

In , compute the orthogonal projection of the point on the plane determined by the points

, and .

Reply: the projection is ( , , ).


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Description: collection of exercises on orthogonal projection and distance. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games

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