Question

Calculate k(t) when r(t) = <4t^-1,-6,6t>

Thank you!

Answer 1

Compute the curvature K(t), using the following expression.

The first step, is to determine the first derivative of the vector r(t), as follows.

The second step, is to calculate the second derivative of the vector r(t), by calculating the first derivative over r'(t).

Then, determine the cross product between r'(t) and r''(t).

Next, calculate the magnitude of the cross product, as follows.  

And the magnitude of the first derivative of the vector r(t) is.

Finally, make the corresponding substitution in the curvature expression.

Hence, the curvature of the vector r(t) is.