Question
Find $\mathbf{C}$ if $\mathbf{r}(t)=\left\langle e^{t}, 3 \cos t, t+10\right\rangle+\mathbf{C}$ and $\mathbf{r}(0)=\langle 0,0,0\rangle$
Step 1
Step 1: First, we substitute $t=0$ into the given vector function $\mathbf{r}(t)$: \[\mathbf{r}(0)=\left\langle e^{0}, 3 \cos 0, 0+10\right\rangle+\mathbf{C} = \langle 1,3,10 \rangle + \mathbf{C}\] Show more…
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