Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (4, -5, 4) and parallel to the vector <1, 5, -2/3> r(t) = (x(t), y(t), z(t)) =
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Since the line is parallel to the vector $\begin{pmatrix} 1 \\ 5 \\ 3 \end{pmatrix}$, we can write the vector equation as: $$\vec{r}(t) = \begin{pmatrix} 4 \\ -5 \\ 4 \end{pmatrix} + t\begin{pmatrix} 1 \\ 5 \\ 3 \end{pmatrix}$$ Now, we can find the parametric Show more…
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