Question

find the unit tangent vector of the given curve r(t)=12t^6i-4t^6j+3t^6k

Answer 1

start with the derivative r'(t) = (72t^5)i-(24t^5)j+(18t^5)k... right?

Answer 2

yeah thats right

Answer 3

after that we need [r'(t)] which would equal sqrt(72^2 + 24^2 + 18^2)... still heading in the right direction?

Answer 4

so the unit tangent vector should be (72t^5)/78 i - (24t^5)/78 j + (18t^5)/78 k

Answer 5

thank you