How Do You Calculate the Binormal Vector B(t) for a Given Curve?

[S-C-3-1-3]

Hi! :)

The question is for r (t) =<t, 4-t2, 0>, find N(t),T(t), and B(t).

First I took the derivative of r (t), and divided it by its length to calculate T(t), which is <1/sqrt(1+4t2),-2t/sqrt(1+4t2,0)>. Then I took the derivative of this using the product rule, and divided it by its length to calculate N(t), which is <-2t/sqrt(1+4t2),-1/sqrt(1+4t2),0)>.

Taking the cross product of these two gives the binormalvector, which is <0,0,0>.

Is this done correctly, or does anyone get a different answer?


Thanks in advance! I didn't do all of the work on here, but I hope that's okay, as I have already done the work to find the answer...?

 

[SammyS]

Show the steps for finding N(t). You have an error in this.

The cross-product is not zero. Did you take the scalar product?