Answer
$\dfrac{\sqrt 6}{2(3t^2+1)^2}$
Work Step by Step
Solve $r'(t)=2\sqrt6ti+2j+6t^2k$ ; $r''(t)=2\sqrt6i+12tk$
This yields, $|r'(t)|=\sqrt {(2\sqrt6t)^2+(2)^2+(6t^2)^2}$
or, $|r'(t)|=6t^2+2$
Write Theorem 10.
$\dfrac{|r'(t) \times r''(t)|}{|r'(t)|^3}=\dfrac{| (2\sqrt6ti+2j+6t^2k)\times(2\sqrt6i+12tk|}{|6t^2+2|^3}$
or, $=\dfrac{|24t-12\sqrt 6 t^2j-4\sqrt6 k|}{|6t^2+2|^3}$
or, $=\dfrac{\sqrt{(24)^2+(-12\sqrt 6 t^2)^2+(-4\sqrt6)^2}}{|6t^2+2|^3}$
or, $=\dfrac{\sqrt 6}{(6t^2+2)^3}$
or, $=\dfrac{\sqrt 6}{2(3t^2+1)^2}$
