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In each case find the tangent vector v or explain why it doesn't exist.

(i) a unit vector v such that K(v)=-3 where K is normal curvature function

(ii)unit vector v such that K(v)=10

(iii) a vector v (possibly non unit) such tha K(v)=12

for (i) and (ii) I found a quartic equation and found for (i) there is a solution but in (ii) the solutions were complex. My problem is this was quite hard work, plus for (iii) I would not have the condition that the sum of the squares of the components of v is 1, thus I would have one equation in 2 unknowns. So what to do?