Question

Find a set of parametric equations of the line. (Enter your answers as a comma-separated list.)

The line passes through the point {eq}\displaystyle (-7,\ 4,\ 5) {/eq} and is perpendicular to the plane given by {eq}\displaystyle -x + 7 y + z = 4 {/eq}.

Answer 1

eq}\displaystyle x(t) = -7 - t \ y(t) = 4 + 7t \ z(t) = 5 + t {/eq}

or in vector form:

{eq}\displaystyle \mathbf{r}(t) = \begin{pmatrix} -7 \ 4 \ 5 \end{pmatrix} + t\begin{pmatrix} -1 \ 7 \ 1 \end{pmatrix} {/eq}