Chapter 13.5, Problem 6E

To determine

Find the acceleration vector a in the form $a=a_{\text{T}}T+a_{\text{N}}N$ at the value of t without finding T and N for the given vector $r\left(t\right)=\left(e^t\cos t\right)i+\left(e^t\sin t\right)j+\sqrt{2}{e}^{t}k,t=0$.