A particle is moving through space with acceleration \(\vec{…
A particle is moving through space with acceleration \(\vec{a}(t)=\langle e^t,0,-6t\rangle\) at time \(t\). At time \(t=0\), the particle is at initial point (1,0,-1) and has initial velocity \(\langle 1,1,0\rangle\). Find the position of the particle at time \(t=1\). Enter the x-component in the first answer box, y-component in the second box and z-component in the third box, without brackets, parentheses or spaces. \(\vec{r}(1)=\langle\) , , \(\rangle\).