# Curvature question

1. Feb 25, 2010

### FreedayFF

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

Find the unit tangent, normal and binormal vectors T,N,B , and the curvature of the curve
x=−4t y=−t2 z=−2t3 at t=1.

2. Relevant equations

3. The attempt at a solution

I found T=(-4/sqrt(56),-2/sqrt(56),-6/sqrt(56)) which is correct. But I keep getting N wrong? PLease help me, thank you!

2. Feb 25, 2010

### LCKurtz

Looks good as far as it goes. Hard to say what you are doing wrong unless you show us what you are doing to get N.

3. Feb 25, 2010

### FreedayFF

N = T'/|T'|
so the first term should be 0; but the webwork keeps denying that answer.

4. Feb 26, 2010

### FreedayFF

N = (0,-2/sqrt(148),-12/sqrt(148)) and that gives a wrong answer

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Last edited: Feb 26, 2010
5. Feb 26, 2010

### cronxeh

Not 100% sure of this (im at work), but you get the train of thought:
r(t) = (-4t)i + (-t^2)j + (-2*t^3)k

v(t) = r'(t) = (-4)i -(2*t)j - (6*t^2)k
||v(t)|| = sqrt(2*(4+t^2+9*t^4))

T(t) = v(t)/||v(t)|| =((-4)i + (-2*t)j + (-6t^2))/sqrt(2*(4+t^2+9*t^4))

Evaluate at t=1

T(1) = ((-4)i + (-2)j + (-6)k)/(6503/869) = 869*(-4i-2j-6k)/6503

N(t) = T'(t)/||T'(t)|| = diff(T,t)/length(diff(T,t))

N(t) = 0i - (2/3) j - (4*t)k
evaluate at t=1

N(1) = 0i - 2/3j -4k

B=T x N = [ 4*t^2, -16*t, 8/3]
at t=1

B(1) = 4i - 16j + 8/3k

6. Feb 26, 2010

### FreedayFF

I believe your answers are incorrect, as I have all T,B, curvature correct in the attached image above. Your T, however, has the same i value as mine, which is 0 and incorrect.

7. Feb 26, 2010

### cronxeh

T=[-0.53454,-0.26727,-0.80181]
N=[0.81053,0.10665,-0.57592]
B=[0.23942,-0.95771,0.15962]

Maple rules.

8. Feb 26, 2010

### FreedayFF

Okay Maple rules do give correct answers. Thanks. But I don't understand why they would give different answers to the "conventional" methods. I'm confused about when to use Maple rules and when not?

9. Feb 26, 2010

### cronxeh

I made a mistake earlier while using the conventional method. The correct way is:

N(t) = T'(t)/||T'(t)|| = (r'(t) x (r''(t) x r'(t)))/(||r'(t)||*||r''(t) x r'(t)||) = <304/(8*sqrt(157)*sqrt(14)), 40/(8*sqrt(157)*sqrt(14)), -216/(8*sqrt(157)*sqrt(14))>

DUH. It all checks out.