Chapter 12, Problem 21RE

a)

To determine

To calculate: The higher order differentiation $r^{\prime }\left(t\right)$ of vector-valued function

$r\left(t\right)=2t^{3}i+4tj-t^{2}k$.

b)

To determine

To calculate: The value of $r^{″}\left(t\right)$ for vector-valued function is $r\left(t\right)=2t^{3}i+4tj-t^{2}k$.

c)

To determine

To calculate: The value of $r^{\prime }\left(t\right)\cdot r^{″}\left(t\right)$ for vector-valued function is $r\left(t\right)=2t^{3}i+4tj-t^{2}k$.

d)

To determine

To calculate: The value of $r^{\prime }\left(t\right)\times r^{″}\left(t\right)$ for vector-valued function is $r\left(t\right)=2t^{3}i+4tj-t^{2}k$.