Question

Find parametric equations for the line. (use the parameter t.) the line of intersection of the planes x y z = 6 and x z = 0

Answer 1

Let
`x=t`. Then

`x+z = 0 \implies z = -x = -t`

`x + y + z = 6 \implies y = 6 - x - z = 6 - t - (-t) = 6`

so our parametric equations for the line are

`\begin{cases}x(t) = t \\ y(t) = 6 \\ z(t) = -t\end{cases}`

where
`t\in\Bbb R`.