Find the curvature of x = e^(t)

[brendan]

Homework Statement

Find the curvature of x = e^(t) y = e^(-t) z = t t = 0

Homework Equations

I've used the equation of

k(t) = |r'(t) x r''(t) |/ |r'(t)|^3

The Attempt at a Solution

k(t) = |r'(t) x r''(t) |/ |r'(t)|^3


= |e^t i + -e^(-t)j + 1k| x |e^t i + e^(-t)j + 0k| / |e^t i + -e^(-t)j + 1k|^3

= |-e^(-t)i + e^(t)j +2k| / |e^t i + -e^(-t)j + 1k|^3

Using t = 0


= |-e^(0)i + e^(0)j +2k| / |e^0 i + -e^(0)j + 1k|^3


= 2/1

= 2

Is this right ?

regards
Brendan

 

[cristo]

I agree with everything to your penultimate line. The modulus of (-1,1,2) is not 2.

 

[brendan]

How about now?

= |-e^(0)i + e^(0)j +2k| / |e^0 i + -e^(0)j + 1k|^3


= sqrt(2)/3


Brendan

 

[cristo]

Looks good to me.

 

[brendan]

Thanks mate!

Brendan