I ime Remaining 12 Essay 5 points Find the equation of the line passing through \( \overrightarrow{r_{0}}=<8,0,-8> \) with direction vector \( \vec{v}=<-3,4,-7> \). Just state your answer. Edit View Insert Format Tools Table 12pt \( \vee \quad \) Paragraph \( \vee \) B \( I \underline{U} \) A 8 p Previous

The equation of the line passing through the point \( \overrightarrow{r_{0}} = \langle 8, 0, -8 \rangle \) with direction vector \( \vec{v} = \langle -3, 4, -7 \rangle \) can be expressed in parametric form as follows: \[ \overrightarrow{r}(t) = \overrightarrow{r_{0}} + t \vec{v} \] Substituting the known values: \[ \overrightarrow{r}(t) = \langle 8, 0, -8 \rangle + t \langle -3, 4, -7 \rangle \] This results in: \[ \overrightarrow{r}(t) = \langle 8 - 3t, 0 + 4t, -8 - 7t \rangle \] Thus, the equation of the line is: \[ \overrightarrow{r}(t) = \langle 8 - 3t, 4t, -8 - 7t \rangle \]