,
,
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. Serveur Wims de l'ESPE-Nice-Toulon - Université de Nice - Sophia Antipolis
- Keywords: interactive mathematics, interactive math, server side interactivity, geometry, euclidean geometry, plane, line, projection, distance, orthogonal, parallel