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#1 2013-06-24 00:44:46

ShivamS
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Registered: 2011-02-07
Posts: 3,519

Tangent Vector practice problems

Please check the following.

Vector r = (e^3t, sin(2t), t^2)


What is vector r(t) prime? I am getting (3e^3t, 2cos(2t), 2t)

Compute the unit tangent vector T(t) and do not simplify the answer. I get vector T(t) = (3e^3t, 2cos(2t), 2t) divided by square root of (9e^6t + 4cos^2(2t) +4t^2)

Thanks in advance.

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#2 2013-06-24 01:06:47

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,410

Re: Tangent Vector practice problems

That look correct! smile


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#3 2013-06-24 01:41:33

ShivamS
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Registered: 2011-02-07
Posts: 3,519

Re: Tangent Vector practice problems

Thanks a lot.

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#4 2013-06-24 02:34:15

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,410

Re: Tangent Vector practice problems

You're welcome.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#5 2013-06-24 02:52:04

ShivamS
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Registered: 2011-02-07
Posts: 3,519

Re: Tangent Vector practice problems

More stuff: g(t) = 4t+1  what is d/dt r(g9t))

I get 4{3e^3(4t+1), 2cos[2(4t+1)], 2(4t+1)}

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#6 2013-06-24 04:24:41

bob bundy
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Registered: 2010-06-20
Posts: 6,313

Re: Tangent Vector practice problems

hi

r(g9t)) I take it that's r(g(t)) so chain rule

dr/dt = dr/dg x dg/dt

Take the first component.  I'm thinking that is

Or am, I mixing up here?

so

diff gives



Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2013-06-24 04:26:29

ShivamS
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Registered: 2011-02-07
Posts: 3,519

Re: Tangent Vector practice problems

d/dt r(g(t)) = g'(t)r'(g(t)) = d/dt(4t+1)r'(4t+1)

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#8 2013-06-24 04:27:05

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,410

Re: Tangent Vector practice problems

Hi Shivamcoder3013

I would say that is correct as well.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#9 2013-06-24 04:27:40

bob bundy
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Registered: 2010-06-20
Posts: 6,313

Re: Tangent Vector practice problems

Sorry I put an edit in above.

Please look.  smile

Back later

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#10 2013-06-24 04:28:49

ShivamS
Member
Registered: 2011-02-07
Posts: 3,519

Re: Tangent Vector practice problems

Thanks.

Last edited by Shivamcoder3013 (2013-06-24 04:28:56)

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#11 2013-06-24 05:31:03

bob bundy
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Registered: 2010-06-20
Posts: 6,313

Re: Tangent Vector practice problems

hi Shivamcoder3013

Your notation is confusing me.  I'd do this like this:

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#12 2013-06-24 09:42:13

ShivamS
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Registered: 2011-02-07
Posts: 3,519

Re: Tangent Vector practice problems

That is not different from my answer.

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#13 2013-06-24 19:14:18

bob bundy
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Registered: 2010-06-20
Posts: 6,313

Re: Tangent Vector practice problems

hi Shivamcoder3013

Oh, that's a big relief for me.  Somehow, I missed that.  Sorry I've dragged this thread out longer than was necessary  smile

Bob.


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#14 2013-06-26 11:59:14

ShivamS
Member
Registered: 2011-02-07
Posts: 3,519

Re: Tangent Vector practice problems

No problem. Thanks both of you.

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