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#1 2014-07-15 00:39:18

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,832
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PerpendicularQ

Given the equation of two lines in 3-space, how do I know they are perpendicular?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#2 2014-07-15 04:54:25

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,363

Re: PerpendicularQ

Determine if they intersect and if the dot product of the directional vectors are 0.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2014-07-15 05:05:24

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,832
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Re: PerpendicularQ

How do I do this?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#4 2014-07-15 05:11:46

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,363

Re: PerpendicularQ

Which part?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2014-07-15 05:14:37

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,832
Website

Re: PerpendicularQ

the second part.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#6 2014-07-15 05:19:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,363

Re: PerpendicularQ

The dot product of two vectors?


{3, 4, 5}.{a, b, c}

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#7 2014-07-15 12:11:37

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,832
Website

Re: PerpendicularQ

I think I will be given the two lines in the form of two equations


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#8 2014-07-15 15:22:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,363

Re: PerpendicularQ

Yes, but you asked for how to do the dot product.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#9 2014-07-15 19:38:29

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,832
Website

Re: PerpendicularQ

How do i do the dot product when the equations of lines are given?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#10 2014-07-16 00:11:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,363

Re: PerpendicularQ

Is it already in parametric form or cartesian?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#11 2014-07-16 00:15:26

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,832
Website

Re: PerpendicularQ

it is like x+y=0 and x+z=0


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#12 2014-07-16 00:21:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,363

Re: PerpendicularQ

Okay that is Cartesian. Do you know how to put it into parametric form?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#13 2014-07-16 00:29:28

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,832
Website

Re: PerpendicularQ

Depends on what you mean by parametric


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#14 2014-07-16 00:29:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,363

Re: PerpendicularQ

All in terms of the parameter t.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#15 2014-07-16 00:33:51

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,832
Website

Re: PerpendicularQ

The first is z=t


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#16 2014-07-16 00:39:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,363

Re: PerpendicularQ

Simple example:

y = 1 - x , put into parametric form.

Say x = t now y = 1 - t

Do you see an advantage of this?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#17 2014-07-16 00:41:33

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,832
Website

Re: PerpendicularQ

I do not.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#18 2014-07-16 00:50:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,363

Re: PerpendicularQ

Good, you are well on your way to seeing how ridiculous the whole vector idea is.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#19 2014-07-16 01:00:43

ShivamS
Member
Registered: 2011-02-07
Posts: 3,514

Re: PerpendicularQ

smile

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#20 2014-07-16 01:01:07

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,832
Website

Re: PerpendicularQ

It is not.

How do I show that xy+x+y=0 and xz+x+z=0 are perpendicular?

Last edited by Agnishom (2014-07-16 01:01:50)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#21 2014-07-16 01:14:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,363

Re: PerpendicularQ

That is not a beginning problem. I do not know how to find the directional derivative of that. or if you should.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#22 2014-07-16 01:30:45

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,832
Website

Re: PerpendicularQ

Ok, here is the problem.

show that all the angles of the internal vertices of at least one of the  spherical triangles formed by the intersection of x^2+y^2=r^2 and x^2+z^2=r^2 and y^2+z^2=r^2  on x^2+y^2+z^2=r^2 is pi/2


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#23 2014-07-16 01:40:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,363

Re: PerpendicularQ

When it comes to vector calculus I am considered to be the idiot of the family. I have no idea how to solve that. If you can not do basics why are you looking at a brilliant problem?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#24 2014-07-16 01:48:35

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,832
Website

Re: PerpendicularQ

I did not borrow this problem from Brilliant.

Triangle_sph%C3%A9rique.svg


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#25 2014-07-16 01:57:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,363

Re: PerpendicularQ

Where does it come from?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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