Difficulty Calculating the Principal Unit Normal Vector.

Hi,

I am having difficulties find the principal unit normal vector N(t) for the vector function

.

I have worked up to this point:

I know that I need to take the derivative of this, and devide it by its length to find the princiipal normal vector; however, I am not sure how to do this!

Thanks!

Re: Difficulty Calculating the Principal Unit Normal Vector.

I have either made progress or gone the wrong direction. Either way, here is the work that I have done since I made this question:

I first factored the , leaving <1,-2t,0> as the vector. Then, to multiply the two, I set as “u” and <1,-2t,0> as “v” to use the product rule. I found the derivative of “u” to be , which further simplifies to , which I multiplied against the scalar. I did the same with taking the derivative of the vector, and multiplying it by the .

At the end, I know have:

Re: Difficulty Calculating the Principal Unit Normal Vector.

Quote:

Originally Posted by

**SC313** Hi,

I am having difficulties find the principal unit normal vector N(t) for the vector function

.

I have worked up to this point:

I know that I need to take the derivative of this, and devide it by its length to find the princiipal normal vector; however, I am not sure how to do this!

Thanks!

Divide this by it's magnitude.

Re: Difficulty Calculating the Principal Unit Normal Vector.

Quote:

Originally Posted by

**SammyS**
Divide this by it's magnitude.

Where do you get this from? Thanks!

Re: Difficulty Calculating the Principal Unit Normal Vector.

Quote:

Originally Posted by

**SC313** Where do you get this from? Thanks!

I took the derivative of **T**(t) that you had in your OP.

Re: Difficulty Calculating the Principal Unit Normal Vector.

Okay, I see now. And how do I find the magnitude of this..., and divide the number by this? :( It's so confusing. thanks by the way

Re: Difficulty Calculating the Principal Unit Normal Vector.

Magnitude: Square root of the sum of the squares of the components.

At least they have a common denominator.