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wholegrain
 Post subject: For what values of a and b are these two vectors collinear (
PostPosted: Mon, 20 Feb 2012 06:46:37 UTC 
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I'd like to know what the steps. I don't really care about the answer.

t = (3a -4b +5, 5b -2a -8)
v = (-3, 4)

t and v are vectors
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outermeasure
 Post subject: Re: For what values of a and b are these two vectors colline
PostPosted: Mon, 20 Feb 2012 10:10:47 UTC 
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wholegrain wrote:
I'd like to know what the steps. I don't really care about the answer.

t = (3a -4b +5, 5b -2a -8)
v = (-3, 4)

t and v are vectors


If \mathbf{t}=(t_1,t_2) and \mathbf{v}=(v_1,v_2) are collinear, then t_1:t_2=v_1:v_2, so ...

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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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wholegrain
 Post subject: Re: For what values of a and b are these two vectors colline
PostPosted: Mon, 20 Feb 2012 14:54:16 UTC 
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The teacher gave the answer, but I have no idea what he did.

Basically, he wrote 6a -b -4 = 0

then he isolated b, which gives:

b = 6a -4

then he somehow came with

the answer, which is, like I said:

t = 7(a-1)(-3,4) or 7(a-1)vector z.

I have no idea what the teacher did.
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Justin
 Post subject: Re: For what values of a and b are these two vectors colline
PostPosted: Mon, 20 Feb 2012 16:36:51 UTC 
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wholegrain wrote:
The teacher gave the answer, but I have no idea what he did.

Basically, he wrote 6a -b -4 = 0

then he isolated b, which gives:

b = 6a -4

then he somehow came with

the answer, which is, like I said:

t = 7(a-1)(-3,4) or 7(a-1)vector z.

I have no idea what the teacher did.


I would just use Outermeasure's ratio argument...

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wholegrain
 Post subject: Re: For what values of a and b are these two vectors colline
PostPosted: Mon, 20 Feb 2012 17:57:44 UTC 
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http://www.google.ca/search?q=Outermeas ... =firefox-a

what's that?

Can you explain how he did it?
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Shadow
 Post subject: Re: For what values of a and b are these two vectors colline
PostPosted: Mon, 20 Feb 2012 18:00:13 UTC 
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wholegrain wrote:
http://www.google.ca/search?q=Outermeasure+RATIO%3F&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a

what's that?

Can you explain how he did it?


No, outermeasure is not a person, it's one of our users who responded to you. Did you read his post? It describes exactly how to do this problem.

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daveyinaz
 Post subject: Re: For what values of a and b are these two vectors colline
PostPosted: Mon, 20 Feb 2012 18:30:35 UTC 
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Or you can do something like so...

3a -4b +5 = -3x
5b -2a -8 = 4x

Get x only on the RHS, set equations equal to each other find b in terms of a.
-a + \frac{4}{3}b - \frac{5}{3} = \frac{5}{4}b - \frac{1}{2}a - 2

plug that back into one of the original equations to get x in terms of a.

This might be similar to what your teacher did.
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wholegrain
 Post subject: Re: For what values of a and b are these two vectors colline
PostPosted: Mon, 20 Feb 2012 21:07:07 UTC 
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Shadow wrote:
wholegrain wrote:
http://www.google.ca/search?q=Outermeasure+RATIO%3F&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a

what's that?

Can you explain how he did it?


No, outermeasure is not a person, it's one of our users who responded to you. Did you read his post? It describes exactly how to do this problem.


I am asking because obviously I have never heard of it.
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wholegrain
 Post subject: Re: For what values of a and b are these two vectors colline
PostPosted: Mon, 20 Feb 2012 21:41:03 UTC 
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the question states for what value of a and b, but how come the answer is 7(a-1)?

so b = 0 and a = R?
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Shadow
 Post subject: Re: For what values of a and b are these two vectors colline
PostPosted: Mon, 20 Feb 2012 22:21:43 UTC 
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wholegrain wrote:
Shadow wrote:
wholegrain wrote:
http://www.google.ca/search?q=Outermeasure+RATIO%3F&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a

what's that?

Can you explain how he did it?


No, outermeasure is not a person, it's one of our users who responded to you. Did you read his post? It describes exactly how to do this problem.


I am asking because obviously I have never heard of it.


Ah, then you shouldn't have included the google search, it made it seem like you thought this was some famous argument with a special name you had searched for but had been unable to find.

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