# Homework Help: Curvature of r(t) = (3 sin t) i + (3 cos t) j + 4t k

1. Oct 30, 2016

1. The problem statement, all variables and given/known data

find the curvature of the vector valued function r(t) = 3sint i + 3cost j +4t k
2. Relevant equations

3. The attempt at a solution
For the unit tangent vector , i got T(t) = (3cost i -3sint j +4k) / sqrt (9 ((sint)^2 ) + 9 ((cost)^2 ) + 4^2 ) =
(3cost i -3sint j +4k) / 5

For the principal unit vector , N(t) , i got -3sint i -3cost j ) / sqrt (9 ((sint)^2 ) + 9 ((cost)^2 )
= -sint i -cost j

We can conclude that |r'(t) | = 5 , |T'(t) | = 3 , so , curvature = |T'(t) | / |r'(t) | = 3/5 , but the ans is 3/25 , which part of my working is wrong ?

Last edited by a moderator: Oct 30, 2016
2. Oct 30, 2016

### PeroK

You need $|\hat{T}'|$ not $|T'|$.

Last edited by a moderator: Oct 30, 2016
3. Oct 30, 2016

what's the difference between $|\hat{T}'|$ and $|T'|$ ???

4. Oct 30, 2016

### PeroK

The first is the time derivative of the unit tangent vector. The second is the time derivative of the tangent vector.

5. Oct 30, 2016

Unit tangent vector and tangent vector are not the same ?

6. Oct 30, 2016

### PeroK

No, why would they be? The tangent vector can have any length.

7. Oct 30, 2016

so , how to get time derivative of the tangent vector. ?

8. Oct 30, 2016

### PeroK

It's the time derivative of the unit tangent vector you want. You just calculate the unit tangent vector, then differentiate it.

9. Oct 30, 2016

do you mean it's |T'(t) | ? if so , then my ans of |T'(t) | is 3 , since k = |T'(t) | / |r'(t) | , so i gt k = 3/5 , but not 3/25

10. Oct 30, 2016

### PeroK

That's just what you did the first time! You need to differentiate $\hat{T}$.

11. Oct 30, 2016

removed

12. Oct 30, 2016

do you mean differentiate |T| to get |T'(t) | ?

If so , then my |T'(t) | = 3

13. Oct 30, 2016

### PeroK

What happened to the $1/5$?

14. Oct 30, 2016

1/5 ???
i dont have 1/5 in my working

15. Oct 30, 2016

### PeroK

Yes you do!

16. Oct 30, 2016

OK , but I didn't get 3 /25 . . . .

17. Oct 30, 2016

### PeroK

That's because you dropped the 1/5!!!!!!

18. Oct 31, 2016

ok , i have tried in another way , but i didnt get the ans though ...
here's my ans , i gt k = 0.1357

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• ###### IMG_20161031_142025.jpg
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19. Oct 31, 2016

for the previous question , i gt the question already , thanks!

20. Nov 1, 2016

bump , what's wrong with my working ?

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