Find the Principal unit normal vector to the curve at the specified value of the parameter.

Question

r(t)=ti+t^(2)j+lntk, t=1

Answer 1

r'(t) = i + 2t j + 1/t k
T(t) = r'/|r'| = (i+2tj+1/t k)/√(1+4t^2+1/t^2)
T(1) = (i+2j+k)/√6

the unit normal vector is
N(t) = T'/|T'|