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ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Tangent Vector practice problems

That look correct!

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“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
The knowledge of some things as a function of age is a delta function.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Tangent Vector practice problems

Thanks a lot.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

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)}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

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

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Tangent Vector practice problems

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Tangent Vector practice problems

Sorry I put an edit in above.

Please look. 

Back later

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Tangent Vector practice problems

Thanks.

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Tangent Vector practice problems

hi Shivamcoder3013

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

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Tangent Vector practice problems

That is not different from my answer.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

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 

Bob.

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Tangent Vector practice problems

No problem. Thanks both of you.