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roshan2004
 Post subject: Differentiation of vectors
PostPosted: Fri, 15 Jul 2011 22:41:19 UTC 
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Please suggest me the solution of the attachment given below
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Shadow
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PostPosted: Fri, 15 Jul 2011 23:09:53 UTC 
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This belongs in physics, topic moved.

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Shadow
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PostPosted: Fri, 15 Jul 2011 23:12:12 UTC 
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As for your question, the cross product always gives you a vector perpendicular to the things you're crossing, so F being perpendicular to v is free. Note that B is constant magnitude, so F is constant iff v is and show one of the two is.

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roshan2004
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PostPosted: Sat, 16 Jul 2011 00:42:39 UTC 
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I have to use the vector calculus to solve and prove it.......................?
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outermeasure
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PostPosted: Sat, 16 Jul 2011 04:25:35 UTC 
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roshan2004 wrote:
I have to use the vector calculus to solve and prove it.......................?


No, you don't need div, grad, or curl to prove it.

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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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