Why is there unique plane which passes through given point and is parallel to given lineFind an equation for the plane that contains the following line and passes through point PEquation of a plane passing through a line and a separate point.Find plane which parallel to two vectors $L_1 ( 3,1,10)$ and $L_2(1,-1,1)$ passes through a point $M(7,-10,3)$Find the equation of the plane that passes through the line of intersection of the planes…Line equation through point, parallel to plane and intersecting lineEquation of a plane given one point and two planesEquation of plane passing through intersection of line and planeEquation of plane through a point and perpendicular to planesFind the Point Through which the Variable Line PassesGiven a plane and a point, find a line that passes through the point and is parallel to the plane
Weird lines in Microsoft Word
Exposing a company lying about themselves in a tightly knit industry: Is my career at risk on the long run?
Homology of the fiber
Would this string work as string?
When should a starting writer get his own webpage?
label a part of commutative diagram
Do I need an EFI partition for each 18.04 ubuntu I have on my HD?
Can a university suspend a student even when he has left university?
DisplayForm problem with pi in FractionBox
What (if any) is the reason to buy in small local stores?
Friend wants my recommendation but I don't want to
Hot air balloons as primitive bombers
The English Debate
Why is there so much iron?
Is this Pascal's Matrix?
What is 管理しきれず?
Why are there no stars visible in cislunar space?
Single word to change groups
Error in master's thesis, I do not know what to do
Why I don't get the wanted width of tcbox?
Does fire aspect on a sword, destroy mob drops?
Do people actually use the word "kaputt" in conversation?
Why doesn't the fusion process of the sun speed up?
Print last inputted byte
Why is there unique plane which passes through given point and is parallel to given line
Find an equation for the plane that contains the following line and passes through point PEquation of a plane passing through a line and a separate point.Find plane which parallel to two vectors $L_1 ( 3,1,10)$ and $L_2(1,-1,1)$ passes through a point $M(7,-10,3)$Find the equation of the plane that passes through the line of intersection of the planes…Line equation through point, parallel to plane and intersecting lineEquation of a plane given one point and two planesEquation of plane passing through intersection of line and planeEquation of plane through a point and perpendicular to planesFind the Point Through which the Variable Line PassesGiven a plane and a point, find a line that passes through the point and is parallel to the plane
$begingroup$
I was trying to solve one question which is asking to find a plane which passes through given point and is parallel to given line.
The given point is $M(2,-5,3)$ and the given line is given as an interesection of the planes $2x-y+3z-1=0 text and 5x+4y-z-7=0$
It is still unclear for me why there is only one unique plane which can be answer, I think that there are more possible planes that can be answers to this.
analytic-geometry
asked Mar 13 at 9:51
someone123123someone123123
445414
$endgroup$
add a comment |
$begingroup$
I was trying to solve one question which is asking to find a plane which passes through given point and is parallel to given line.
The given point is $M(2,-5,3)$ and the given line is given as an interesection of the planes $2x-y+3z-1=0 text and 5x+4y-z-7=0$
It is still unclear for me why there is only one unique plane which can be answer, I think that there are more possible planes that can be answers to this.
analytic-geometry
asked Mar 13 at 9:51
someone123123someone123123
445414
$endgroup$
$begingroup$
Perhaps you might include the specific problem that you’re asking about.
$endgroup$
– amd
Mar 13 at 19:40
$begingroup$
I inserted the given point and the line into the post
$endgroup$
– someone123123
Mar 13 at 20:30
$begingroup$
Are you sure that the problem said for the plane to be parallel to that line? If it must instead include the line, then the solution is be unique.
$endgroup$
– amd
Mar 13 at 20:35
$begingroup$
Yes, the question is asking about plane which is parallel to the given line.
$endgroup$
– someone123123
Mar 13 at 20:45
add a comment |
$begingroup$
I was trying to solve one question which is asking to find a plane which passes through given point and is parallel to given line.
The given point is $M(2,-5,3)$ and the given line is given as an interesection of the planes $2x-y+3z-1=0 text and 5x+4y-z-7=0$
It is still unclear for me why there is only one unique plane which can be answer, I think that there are more possible planes that can be answers to this.
analytic-geometry
asked Mar 13 at 9:51
someone123123someone123123
445414
$endgroup$
I was trying to solve one question which is asking to find a plane which passes through given point and is parallel to given line.
The given point is $M(2,-5,3)$ and the given line is given as an interesection of the planes $2x-y+3z-1=0 text and 5x+4y-z-7=0$
It is still unclear for me why there is only one unique plane which can be answer, I think that there are more possible planes that can be answers to this.
analytic-geometry
analytic-geometry
asked Mar 13 at 9:51
someone123123someone123123
445414
asked Mar 13 at 9:51
someone123123someone123123
445414
edited Mar 13 at 20:30
someone123123
asked Mar 13 at 9:51
someone123123someone123123
445414
asked Mar 13 at 9:51
someone123123someone123123
445414
asked Mar 13 at 9:51
someone123123someone123123
445414
445414
$begingroup$
Perhaps you might include the specific problem that you’re asking about.
$endgroup$
– amd
Mar 13 at 19:40
$begingroup$
I inserted the given point and the line into the post
$endgroup$
– someone123123
Mar 13 at 20:30
$begingroup$
Are you sure that the problem said for the plane to be parallel to that line? If it must instead include the line, then the solution is be unique.
$endgroup$
– amd
Mar 13 at 20:35
$begingroup$
Yes, the question is asking about plane which is parallel to the given line.
$endgroup$
– someone123123
Mar 13 at 20:45
add a comment |
$begingroup$
Perhaps you might include the specific problem that you’re asking about.
$endgroup$
– amd
Mar 13 at 19:40
$begingroup$
I inserted the given point and the line into the post
$endgroup$
– someone123123
Mar 13 at 20:30
$begingroup$
Are you sure that the problem said for the plane to be parallel to that line? If it must instead include the line, then the solution is be unique.
$endgroup$
– amd
Mar 13 at 20:35
$begingroup$
Yes, the question is asking about plane which is parallel to the given line.
$endgroup$
– someone123123
Mar 13 at 20:45
$begingroup$
Perhaps you might include the specific problem that you’re asking about.
$endgroup$
– amd
Mar 13 at 19:40
$begingroup$
Perhaps you might include the specific problem that you’re asking about.
$endgroup$
– amd
Mar 13 at 19:40
$begingroup$
I inserted the given point and the line into the post
$endgroup$
– someone123123
Mar 13 at 20:30
$begingroup$
I inserted the given point and the line into the post
$endgroup$
– someone123123
Mar 13 at 20:30
$begingroup$
Are you sure that the problem said for the plane to be parallel to that line? If it must instead include the line, then the solution is be unique.
$endgroup$
– amd
Mar 13 at 20:35
$begingroup$
Are you sure that the problem said for the plane to be parallel to that line? If it must instead include the line, then the solution is be unique.
$endgroup$
– amd
Mar 13 at 20:35
$begingroup$
Yes, the question is asking about plane which is parallel to the given line.
$endgroup$
– someone123123
Mar 13 at 20:45
$begingroup$
Yes, the question is asking about plane which is parallel to the given line.
$endgroup$
– someone123123
Mar 13 at 20:45
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Your are right, such plane is not unique. For example the planes $2x-y+3z=18$ and $5x+4y-z=-13$ pass through the point $(2,-5,3)$ and they are parallel to the given line.
More generally, through the given point, there is a unique line parallel to the given line, but then any plane through this second line is parallel to the given line.
answered Mar 13 at 9:55
Robert ZRobert Z
101k1069142
$endgroup$
$begingroup$
I'm thinking like this, but my teacher gave some explanation that I didn't really understand. She says that there is only one such plane
$endgroup$
– someone123123
Mar 13 at 9:57
$begingroup$
Maybe the problem was "find a plane which passes through a given point and it is orthogonal to a given line.
$endgroup$
– Robert Z
Mar 13 at 10:00
$begingroup$
Or perhaps the plane is supposed to include the intersection line of the two given planes (see updated question). Impossible to know without seeing the teacher’s solution.
$endgroup$
– amd
Mar 14 at 0:24
add a comment |
$begingroup$
You are right: there are infinitely mane planes passing through a point and parallel to a given line.
answered Mar 13 at 9:55
AlessioDVAlessioDV
955114
$endgroup$
add a comment |
$begingroup$
As another answer points out, the claim is false. Given a set of planes parallel to each other as well as to the given line, only one of those planes will pass through the given point.
answered Mar 13 at 10:00
Oscar LanziOscar Lanzi
13.2k12136
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3146342%2fwhy-is-there-unique-plane-which-passes-through-given-point-and-is-parallel-to-gi%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Your are right, such plane is not unique. For example the planes $2x-y+3z=18$ and $5x+4y-z=-13$ pass through the point $(2,-5,3)$ and they are parallel to the given line.
More generally, through the given point, there is a unique line parallel to the given line, but then any plane through this second line is parallel to the given line.
answered Mar 13 at 9:55
Robert ZRobert Z
101k1069142
$endgroup$
$begingroup$
I'm thinking like this, but my teacher gave some explanation that I didn't really understand. She says that there is only one such plane
$endgroup$
– someone123123
Mar 13 at 9:57
$begingroup$
Maybe the problem was "find a plane which passes through a given point and it is orthogonal to a given line.
$endgroup$
– Robert Z
Mar 13 at 10:00
$begingroup$
Or perhaps the plane is supposed to include the intersection line of the two given planes (see updated question). Impossible to know without seeing the teacher’s solution.
$endgroup$
– amd
Mar 14 at 0:24
add a comment |
$begingroup$
Your are right, such plane is not unique. For example the planes $2x-y+3z=18$ and $5x+4y-z=-13$ pass through the point $(2,-5,3)$ and they are parallel to the given line.
More generally, through the given point, there is a unique line parallel to the given line, but then any plane through this second line is parallel to the given line.
answered Mar 13 at 9:55
Robert ZRobert Z
101k1069142
$endgroup$
$begingroup$
I'm thinking like this, but my teacher gave some explanation that I didn't really understand. She says that there is only one such plane
$endgroup$
– someone123123
Mar 13 at 9:57
$begingroup$
Maybe the problem was "find a plane which passes through a given point and it is orthogonal to a given line.
$endgroup$
– Robert Z
Mar 13 at 10:00
$begingroup$
Or perhaps the plane is supposed to include the intersection line of the two given planes (see updated question). Impossible to know without seeing the teacher’s solution.
$endgroup$
– amd
Mar 14 at 0:24
add a comment |
$begingroup$
Your are right, such plane is not unique. For example the planes $2x-y+3z=18$ and $5x+4y-z=-13$ pass through the point $(2,-5,3)$ and they are parallel to the given line.
More generally, through the given point, there is a unique line parallel to the given line, but then any plane through this second line is parallel to the given line.
answered Mar 13 at 9:55
Robert ZRobert Z
101k1069142
$endgroup$
Your are right, such plane is not unique. For example the planes $2x-y+3z=18$ and $5x+4y-z=-13$ pass through the point $(2,-5,3)$ and they are parallel to the given line.
More generally, through the given point, there is a unique line parallel to the given line, but then any plane through this second line is parallel to the given line.
answered Mar 13 at 9:55
Robert ZRobert Z
101k1069142
edited Mar 14 at 4:25
answered Mar 13 at 9:55
Robert ZRobert Z
101k1069142
answered Mar 13 at 9:55
Robert ZRobert Z
101k1069142
answered Mar 13 at 9:55
Robert ZRobert Z
101k1069142
101k1069142
$begingroup$
I'm thinking like this, but my teacher gave some explanation that I didn't really understand. She says that there is only one such plane
$endgroup$
– someone123123
Mar 13 at 9:57
$begingroup$
Maybe the problem was "find a plane which passes through a given point and it is orthogonal to a given line.
$endgroup$
– Robert Z
Mar 13 at 10:00
$begingroup$
Or perhaps the plane is supposed to include the intersection line of the two given planes (see updated question). Impossible to know without seeing the teacher’s solution.
$endgroup$
– amd
Mar 14 at 0:24
add a comment |
$begingroup$
I'm thinking like this, but my teacher gave some explanation that I didn't really understand. She says that there is only one such plane
$endgroup$
– someone123123
Mar 13 at 9:57
$begingroup$
Maybe the problem was "find a plane which passes through a given point and it is orthogonal to a given line.
$endgroup$
– Robert Z
Mar 13 at 10:00
$begingroup$
Or perhaps the plane is supposed to include the intersection line of the two given planes (see updated question). Impossible to know without seeing the teacher’s solution.
$endgroup$
– amd
Mar 14 at 0:24
$begingroup$
I'm thinking like this, but my teacher gave some explanation that I didn't really understand. She says that there is only one such plane
$endgroup$
– someone123123
Mar 13 at 9:57
$begingroup$
I'm thinking like this, but my teacher gave some explanation that I didn't really understand. She says that there is only one such plane
$endgroup$
– someone123123
Mar 13 at 9:57
$begingroup$
Maybe the problem was "find a plane which passes through a given point and it is orthogonal to a given line.
$endgroup$
– Robert Z
Mar 13 at 10:00
$begingroup$
Maybe the problem was "find a plane which passes through a given point and it is orthogonal to a given line.
$endgroup$
– Robert Z
Mar 13 at 10:00
$begingroup$
Or perhaps the plane is supposed to include the intersection line of the two given planes (see updated question). Impossible to know without seeing the teacher’s solution.
$endgroup$
– amd
Mar 14 at 0:24
$begingroup$
Or perhaps the plane is supposed to include the intersection line of the two given planes (see updated question). Impossible to know without seeing the teacher’s solution.
$endgroup$
– amd
Mar 14 at 0:24
add a comment |
$begingroup$
You are right: there are infinitely mane planes passing through a point and parallel to a given line.
answered Mar 13 at 9:55
AlessioDVAlessioDV
955114
$endgroup$
add a comment |
$begingroup$
You are right: there are infinitely mane planes passing through a point and parallel to a given line.
answered Mar 13 at 9:55
AlessioDVAlessioDV
955114
$endgroup$
add a comment |
$begingroup$
You are right: there are infinitely mane planes passing through a point and parallel to a given line.
answered Mar 13 at 9:55
AlessioDVAlessioDV
955114
$endgroup$
You are right: there are infinitely mane planes passing through a point and parallel to a given line.
answered Mar 13 at 9:55
AlessioDVAlessioDV
955114
answered Mar 13 at 9:55
AlessioDVAlessioDV
955114
answered Mar 13 at 9:55
AlessioDVAlessioDV
955114
answered Mar 13 at 9:55
AlessioDVAlessioDV
955114
955114
add a comment |
add a comment |
$begingroup$
As another answer points out, the claim is false. Given a set of planes parallel to each other as well as to the given line, only one of those planes will pass through the given point.
answered Mar 13 at 10:00
Oscar LanziOscar Lanzi
13.2k12136
$endgroup$
add a comment |
$begingroup$
As another answer points out, the claim is false. Given a set of planes parallel to each other as well as to the given line, only one of those planes will pass through the given point.
answered Mar 13 at 10:00
Oscar LanziOscar Lanzi
13.2k12136
$endgroup$
add a comment |
$begingroup$
As another answer points out, the claim is false. Given a set of planes parallel to each other as well as to the given line, only one of those planes will pass through the given point.
answered Mar 13 at 10:00
Oscar LanziOscar Lanzi
13.2k12136
$endgroup$
As another answer points out, the claim is false. Given a set of planes parallel to each other as well as to the given line, only one of those planes will pass through the given point.
answered Mar 13 at 10:00
Oscar LanziOscar Lanzi
13.2k12136
edited Mar 13 at 10:06
answered Mar 13 at 10:00
Oscar LanziOscar Lanzi
13.2k12136
answered Mar 13 at 10:00
Oscar LanziOscar Lanzi
13.2k12136
answered Mar 13 at 10:00
Oscar LanziOscar Lanzi
13.2k12136
13.2k12136
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3146342%2fwhy-is-there-unique-plane-which-passes-through-given-point-and-is-parallel-to-gi%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Perhaps you might include the specific problem that you’re asking about.
$endgroup$
– amd
Mar 13 at 19:40
$begingroup$
I inserted the given point and the line into the post
$endgroup$
– someone123123
Mar 13 at 20:30
$begingroup$
Are you sure that the problem said for the plane to be parallel to that line? If it must instead include the line, then the solution is be unique.
$endgroup$
– amd
Mar 13 at 20:35
$begingroup$
Yes, the question is asking about plane which is parallel to the given line.
$endgroup$
– someone123123
Mar 13 at 20:45