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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Which part?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

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

**In mathematics, you don't understand things. You just get used to them.**

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

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Is it already in parametric form or cartesian?

**In mathematics, you don't understand things. You just get used to them.**

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

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.**

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Depends on what you mean by parametric

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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All in terms of the parameter t.

**In mathematics, you don't understand things. You just get used to them.**

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The first is z=t

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

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.**

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I do not.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.**

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**ShivamS****Member**- Registered: 2011-02-07
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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)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

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.**

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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

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.**

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I did not borrow this problem from Brilliant.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,501

Where does it come from?

**In mathematics, you don't understand things. You just get used to them.**

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