I Know it is impossible to do so since the parametric equation for a plane is the intersection of $2$ planes.For example:
$x$ $=$ $\frac{-5}{4t}+\frac{1}{4}$;
$y=\frac{3}{4t}+\frac{5}{4}$;
$z=t$
But when I combine any of the 2 equations above, I can only get the relationship between $x $ and $y$; $x$ and $z$ or $y$ and $z$, that is, $3$ lines in two dimensions. So but the intersection of $2$ planes yields for only $1$ line. So, don't they contradict with one another?
And I also have 2 associated questions:
- How to use the parametric equation of a line in three dimensions to get the equations of intersecting planes?
2.How to use the parametric equation of a line in three dimensions to get the equations of the line derive from the intersection of 2 planes?