Answer
$\dfrac{6t^2}{(9t^4+4t^2)^{3/2}}$
Work Step by Step
As we are given that $r(t)=t^3j+t^2k$
Write Theorem 10.
$\dfrac{|r'(t) \times r''(t)|}{|r'(t)|^3}$
Find $r'(t)=3t^2j+2tk$ and $r''(t)=6tj+2k$
it yields $|r'(t)|=\sqrt {(3t^2)^2+(2t)^2}=\sqrt {9t^4+4t^2}$
Thus,
$\dfrac{|r'(t) \times r''(t)|}{|r'(t)|^3}=\dfrac{| (3t^2j+2tk)\times(6tj+2k)|}{|\sqrt {9t^4+4t^2}|^3}=\dfrac{6t^2}{|\sqrt {9t^4+4t^2}|^3}$
After simplifications, we get $\dfrac{|r'(t) \times r''(t)|}{|r'(t)|^3}=\dfrac{6t^2}{(9t^4+4t^2)^{3/2}}$
