An ant moves along a curve r(t) = < 3sin(t), 4t, 3cos(t) > where t is time, starting at (0,0,3). Find the position vector on the curve after moving 10 units along the curve from the starting point.
What I know:
-I think I have to take the integral from 0 to 10, of r'(t) to get the length after it moved 10 units along the curve
-Starting point could be position vector?
-Component-wise differentiation may be needed to find the position vector
I have tried these steps but still cannot obtain a final answer because I'm not sure what to do. Any guidance or help would be appreciated,
Thanks.