Equation of Plane Question

[vg19]

Hi,

Given the plane 2x + y - z = 4, find its parametric equations.

This question seems simple, but the solution is not coming to me. I know the normal is (2,1,-1). But how do I find out the direction vectors and the points for the parametric equations?

[Parth Dave]

I would suggest finding three points on the plane and create two direction vectors and a point for your parametric equation. The easiest three points would be the intercepts. if y and z are 0, the co-ordinate becomes: (2,0,0). Using a similar process, you can find the two other intercepts, which are:
(2, 0, 0)
(0, 4, 0)
(0, 0, -4)

Thus, you can create two direction vectors and a third point. I think there is an easier way to approach this, but for now it eludes me.