Did I Solve This Exam Prep Problem Correctly?

[mr_coffee]

Hello everyone! I need to seee if i did this problem right...The answer isn't in the back of the book and I'm studying for an exam! here is my work and problem:
http://show.imagehosting.us/show/775021/0/nouser_775/T0_-1_775021.jpg
if that link is slow check this one:
http://img132.imageshack.us/img132/8606/lastscan3kj.jpg
Thanks.

 

[amcavoy]

Hello everyone! I need to seee if i did this problem right...The answer isn't in the back of the book and I'm studying for an exam! here is my work and problem:
http://show.imagehosting.us/show/775021/0/nouser_775/T0_-1_775021.jpg
if that link is slow check this one:
http://img132.imageshack.us/img132/8606/lastscan3kj.jpg
Thanks.

You still didn't answer the question: What would the graph look like?

Alex

 

[mr_coffee]

The problem has alittle calculator sign next to it...so that probably means its hard to graph, and our professor doesn't allow calculators on the exam, so I'm guessing he won't put it on there, but did i do the first part right?

 

[arildno]

First, you have not found the correct expression for the tangent vector at
(1,1,1)
You have been given the POSITION VECTOR FOR THE CURVE:
$$\vec{r}(t)=(t^{2},t^{4},t^{3})$$
What is the general expression for the TANGENT vector at an arbitrary point "t" now?

 

[Dr.Brain]

You know that the tangent will pass through the point (1,1,1) (given in the question) , now for formulating the parametric equation for tangent , you also need the corresponding direction-cosines , Because you know that the corresponding Velocity vector = dr/dt will be parallel to the tangent , you can try differentiating the expression , and put in value of 't' to get the direction-cosines.

BJ

 

[arildno]

You know that the tangent will pass through the point (1,1,1) (given in the question) , now for formulating the parametric equation for tangent , you also need the corresponding direction-cosines , Because you know that the corresponding Velocity vector = dr/dt will be parallel to the tangent , you can try differentiating the expression , and put in value of 't' to get the direction-cosines.

BJ

A quibble:
They won't be direction cosines unless you normalize the tangent vector..