Curvature=|r'(t)xr''(t)|/|r'(t)|^3Find Curvature of r(t)=t*i+(1/2)t^2*j+t^2*k

  • Thread starter Thread starter Math10
  • Start date Start date
  • Tags Tags
    Curvature
Math10
Messages
301
Reaction score
0

Homework Statement


Find the curvature of r(t)=t*i+(1/2)t^2*j+t^2*k.

Homework Equations


None.

The Attempt at a Solution


r'(t)=<1, t, 2t>
r"(t)=<0, 1, 2>
r'(t)xr''(t)=<0, t, 4t>
 
Physics news on Phys.org
Math10 said:

Homework Statement


Find the curvature of r(t)=t*i+(1/2)t^2*j+t^2*k.

Homework Equations


None.

The Attempt at a Solution


r'(t)=<1, t, 2t>
r"(t)=<0, 1, 2>
r'(t)xr''(t)=<0, t, 4t>

You should really state what your question is, but the cross product is wrong.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top