Chapter 12.4, Problem 18ES

To determine

To calculate: The value of $B\left(t\right)$ directly from $r\left(t\right)=a\cos ti+a\sin tj+ctk$ , $\left(a\ne 0,c\ne 0\right)$ by the use of the formula, $B\left(t\right)=T\left(t\right)\times N\left(t\right)$ , and then check the answer by using $B\left(t\right)=\frac{r^{\prime }\left(t\right)\times r^{″}\left(t\right)}{‖r^{\prime }\left(t\right)\times r^{″}\left(t\right)‖}$ .