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How can i answer this question?
Last edited by ottersandseals1; 1 month ago
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#2
(Original post by ottersandseals1)
How can i answer this question? Been stuck on for a while.
If a plane contains two distinct points P1 and P2, show that it contains every point on the line through P1 and P2.
Any help is appreciated
How can i answer this question? Been stuck on for a while.
If a plane contains two distinct points P1 and P2, show that it contains every point on the line through P1 and P2.
Any help is appreciated
Interpret the line segment as a linear combination of P1 and P2 and Interpret the segment in terms of the two points.
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#3
(Original post by ottersandseals1)
How can i answer this question? Been stuck on for a while.
If a plane contains two distinct points P1 and P2, show that it contains every point on the line through P1 and P2.
Any help is appreciated
How can i answer this question? Been stuck on for a while.
If a plane contains two distinct points P1 and P2, show that it contains every point on the line through P1 and P2.
Any help is appreciated
be vectors representing the points P1,P2.A plane with general equation
contains these two points, therefore we have that
The line through P1,P2 is given as
Show that this satisfies the plane's equation, which would hence imply that this line lies entirely in the plane.
Last edited by RDKGames; 2 months ago
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#5
The previous post is a near full solution.
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(Original post by RDKGames)
Let be vectors representing the points P1,P2.
A plane with general equation contains these two points, therefore we have that
The line through P1,P2 is given as
Show that this satisfies the plane's equation, which would hence imply that this line lies entirely in the plane.
Let
be vectors representing the points P1,P2.A plane with general equation
contains these two points, therefore we have thatThe line through P1,P2 is given as
Show that this satisfies the plane's equation, which would hence imply that this line lies entirely in the plane.
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#7
(Original post by ottersandseals1)
Sorry, where does the t come from?
Sorry, where does the t come from?
If you can show all points (for all t) lie on the plane, then you're done.
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(Original post by mqb2766)
t is a free variable between 0 and 1. It generates all points on the line between P1 and P2.
If you can show all points (for all t) lie on the plane, then you're done.
t is a free variable between 0 and 1. It generates all points on the line between P1 and P2.
If you can show all points (for all t) lie on the plane, then you're done.
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#9
(Original post by ottersandseals1)
Do i use the equation r.n = d ? Sorry if it's taking me a while to get
Do i use the equation r.n = d ? Sorry if it's taking me a while to get
r is the point, n is the (unit) normal and d is the distance from the origin.
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(Original post by mqb2766)
That is an equation of the plane. So yes.
r is the point, n is the (unit) normal and d is the distance from the origin.
That is an equation of the plane. So yes.
r is the point, n is the (unit) normal and d is the distance from the origin.
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#11
(Original post by mqb2766)
t is a free variable between 0 and 1. It generates all points on the line between P1 and P2.
If you can show all points (for all t) lie on the plane, then you're done.
t is a free variable between 0 and 1. It generates all points on the line between P1 and P2.
If you can show all points (for all t) lie on the plane, then you're done.
(Original post by mqb2766)
That is an equation of the plane. So yes.
r is the point, n is the (unit) normal and d is the distance from the origin.
That is an equation of the plane. So yes.
r is the point, n is the (unit) normal and d is the distance from the origin.
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#12
(Original post by ottersandseals1)
And from the example above R = (P2 - P1)?
And from the example above R = (P2 - P1)?
But subtracting the two equations shows the difference
(P1-P2).n = 0
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#13
OP, out of curiosity, why did you remove all your posts on your previous threads? Looks a bit dodgy .. almost as if you asked for help with assessed work and want to get rid of the evidence 
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(Original post by RDKGames)
t does not necessarily need to be between 0 and 1.
n is not necessarily the unit normal.
t does not necessarily need to be between 0 and 1.
n is not necessarily the unit normal.
(Original post by mqb2766)
r is either p1 or p2. They satisfy r.n=d
But subtracting the two equations shows the difference
(P1-P2).n = 0
r is either p1 or p2. They satisfy r.n=d
But subtracting the two equations shows the difference
(P1-P2).n = 0
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(Original post by RDKGames)
OP, out of curiosity, why did you remove all your posts on your previous threads? Looks a bit dodgy .. almost as if you asked for help with assessed work and want to get rid of the evidence
OP, out of curiosity, why did you remove all your posts on your previous threads? Looks a bit dodgy .. almost as if you asked for help with assessed work and want to get rid of the evidence
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#16
(Original post by ottersandseals1)
Does that mean t can be n then?
Does that mean t can be n then?
Which equation of a plane are you happy using?
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#17
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#18
(Original post by ottersandseals1)
Sorry which threads are you talking about?
Sorry which threads are you talking about?
https://www.thestudentroom.co.uk/sho....php?t=6733548
https://www.thestudentroom.co.uk/sho....php?t=6732568
https://www.thestudentroom.co.uk/sho....php?t=6732154
https://www.thestudentroom.co.uk/sho....php?t=6686314
etc ...
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#19
(Original post by ottersandseals1)
I think r.n = d is the best, unless you think i could use a better one?
I think r.n = d is the best, unless you think i could use a better one?
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#20
(Original post by ottersandseals1)
So, a is a known vector for a fixed point in a plane, n is the normal vector and r is a resultant vector?
So, a is a known vector for a fixed point in a plane, n is the normal vector and r is a resultant vector?
r is a point (vector) on the plane. Not sure what a or the resultant vector are?
Last edited by mqb2766; 2 months ago
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