Thread: Vector Calculus

I am doing a TNB-Frame problem and I am currently finding the tangent. The point I am trying to find it at is t=0 and my vector T(t) comes out to be in indeterminate form. So my question is how would I solve for vector T(t).

Originally Posted by Sgraveyard

I am doing a TNB-Frame problem and I am currently finding the tangent. The point I am trying to find it at is t=0 and my vector T(t) comes out to be in indeterminate form. So my question is how would I solve for vector T(t).

People will be able to help easier if you post your question, and the work you have done so far.

Vector T(t) = <tcos(t), tsin(t),0>/sqrt(t^2*cos^2(t)+t^2*sin^2(t))

At t=0

R(t) was originally <cos(t)+t*sin(t),sin(t)-t*cos(t),1>

Originally Posted by Sgraveyard

Vector T(t) = <tcos(t), tsin(t),0>/sqrt(t^2*cos^2(t)+t^2*sin^2(t))

At t=0

You need to wrap your latex in MATH codes.

Is your vector $\displaystyle T(t) = (t\cos(t), t\sin(t),0>$, not sure what the $\displaystyle \sqrt{t^2*cos^2(t)+t^2*sin^2(t)}$ is?

Originally Posted by craig

You need to wrap your latex in MATH codes.

Is your vector $\displaystyle T(t) = (t\cos(t), t\sin(t),0>$, not sure what the $\displaystyle \sqrt{t^2*cos^2(t)+t^2*sin^2(t)}$ is?

Sorry about that.

$\displaystyle \sqrt{t^2*cos^2(t)+t^2*sin^2(t)}$ is the magnitude of R'(t). Since $\displaystyle T(t) = R'(t)/|R'(t)|$

So is it the vector $\displaystyle T(t) = (t\cos(t), t\sin(t),0>$ that you want to differentiate?

Originally Posted by craig

So is it the vector $\displaystyle T(t) = (t\cos(t), t\sin(t),0>$ that you want to differentiate?

Nah. I differentiated $\displaystyle R(t)= <cos(t)+t*sin(t),sin(t)-t*cos(t),1>$ into $\displaystyle R'(t)=<t*cos(t),t*sin(t),0>$

My goal is to find vector T(t) which is $\displaystyle R'(t)'/|R'(t)|$

When you do that though you are in indeterminate form. So my question is how would I solve it properly?

Originally Posted by Sgraveyard

Nah. I differentiated $\displaystyle R(t)= <cos(t)+t*sin(t),sin(t)-t*cos(t),1>$ into $\displaystyle R'(t)=<t*cos(t),t*sin(t),0>$

My goal is to find vector T(t) which is $\displaystyle R'(t)'/|R'(t)|$

When you do that though you are in indeterminate form. So my question is how would I solve it properly?

Ahh i do apologise. Do they not give you any limits for the value of $\displaystyle \cos{t}$ or $\displaystyle \sin{t}$ in the question then?

Originally Posted by craig

Ahh i do apologise. Do they not give you any limits for the value of $\displaystyle \cos{t}$ or $\displaystyle \sin{t}$ in the question then?

No problem. Nope, they just say determine TNB-Frame at the point (1,0,1) which is t=0