# 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 .

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