# Find parametric representation for the plane

1. Mar 13, 2013

### dan38

1. The problem statement, all variables and given/known data

Plane: 4x−2y+10z =16.

2. Relevant equations

3. The attempt at a solution

So I've used two parameters, "u" and "v" with x = u and y = v
Re-arranging z in terms of "u" and "v": z = 1.6 - 0.4x + 0.2y
Hence r(t) = (u , v , 1.6 - 0.4 x + 0.2y)
Is this correct?

2. Mar 13, 2013

### vela

Staff Emeritus
Essentially. x and y shouldn't be in your final expression; there should only be u and v.

3. Mar 13, 2013

### dan38

oh yeah, sorry was a typo
but anyway, the solutions say the answer is (10u,10v,−4u+2v+1.6)
which isnt equivalent to my answer...

4. Mar 13, 2013

### vela

Staff Emeritus
They're equivalent. The solutions defined the parameters as x=10u and y=10v.

5. Mar 14, 2013

### dan38

ah I see, thanks!

6. Mar 15, 2013

### HallsofIvy

Personally, I would have got a third answer!
We can easily solve 4x- 2y+ 10z= 16 for y: y= 2x+ 5z- 8.

Now, use x and z as parameters:
x= u
y= 2u+ 5v- 8
z= v