Chapter 12, Problem 22RE

a)

To determine

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

b)

To determine

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

c)

To determine

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

d)

To determine

To calculate: The value of $r^{\prime }\left(t\right)\times r^{″}\left(t\right)$ for the vector-valued function

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