,
,
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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