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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'

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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.

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Which part?

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Yes, but you asked for how to do the dot product.

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**If it ain't broke, fix it until it is.**

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Is it already in parametric form or cartesian?

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
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Okay that is Cartesian. Do you know how to put it into parametric form?

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**If it ain't broke, fix it until it is.**

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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

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The first is z=t

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Simple example:

y = 1 - x , put into parametric form.

Say x = t now y = 1 - t

Do you see an advantage of this?

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I do not.

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,633

Where does it come from?

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**If it ain't broke, fix it until it is.**

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