I have found the equation for unit vector:
T(t) = <2t, 2t^2, 1> / sqrt(4t^2 + 4t^4 + 1)
and it has been verified as correct. I now have to calculate N(t) which I know to be T'(t) / magnitude (T'(t)) at t = -3
so to find a general form for N(t) I did the quotient rule to find T'(t), then plugged in my -3 and I am just getting ridiculous numbers and it's not working out at all.
T'(t) = (4t^2+4t^4+1)^.5 <2, 4t, 0> -
<2t, 2t^2, 1>[.5(4t^2 + 4t^4+1)^-.5)
all over (4t^2 + 4t^4 + 1)
plugging in t = -3
19 < 2, -12, 0 > - < -6, 18, 1> (.5)(1/19)
Simplifying this all gives me horrible numbers...can anyone spot what I'm doing wrong or maybe I'm just messing all the algebra up?
Thanks in advance, I know this is a tedious problem, so I really appreciate the help!