Curvature of a Curve Help?

v
= dr / dt
= i + ( t^2 / 12 ) j

a
= dv / dt
= ( t / 6 ) j

v × a =
[ i.......j........k ]
[ 1...t^2/12...0 ]
[ 0....t/6.......0 ]
= ( t / 6 ) k

∣ v × a ∣ = t / 6
when t = 3
∣ v × a (3) ∣ = 3/6 = 1/2

∣ v ∣ = √ ( 1^2 + t^4/144 )
∣ v (3) ∣
= √ ( 1^2 + 3^4/144 )
= √ [ (144+81) /144 ]
= √ ( 225 / 144 )
= 15/12
= 5/4

Curvature
= κ (3)
= ∣ v × a ∣ / ∣ v ∣^3 , at t = 3
= (1/2) / (5/4)^3
= (1/2) / (125/64)
= 64/250
= 32/125 ..... Ans