Finding a Vector Equation for a Plane with Scalar Equation 2x-y+3z-24=0

[thomasrules]

Find a vector equation for the plane with scalar equation

2x-y+3z-24=0

I have tried but I have no idea at all really how to do it...I have to do it using geometry just to let you know

 

[HallsofIvy]

Solve for y: y= 2x+ 3z-24. Now use x and z as parameters: you can call them s and t if you like:

x= s, y= 2s+ 3t- 24, z= t

Then r(s, t)= si+ (2s+ 3t- 24)j+ tk.

Is that what you mean?