need some help with calculus 3

[skim milk]

I understand everything that is going on so far and I just need to know how to get started with this problem

Problem:
Find equations parallel for the planes to x+3y-1z = 1 and two units away from it.

I'm pretty sure this isn't difficult but the examples we went over in class were slightly different and that's what is confusing me a little.

 

[BrownTown]

I'm to lazy to actually think, but at a random first glance it almost seems like you just go +-2 to the right side.

Edit, except of course no that don't work you would like have to find the line perpendicular to that pland and then go 2 up and down it not just +-2.

 

[jersiq]

I'll just give you a bump.

Two planes are parrallel if their normal vectors are parallel.

For example:

x+2y-3z=4 Hence N1<1,2,-3>
2x+4y-6z=3 Hence N2<2,4,-6>

since 2*(N1)=N2 these planes are parallel.

 

[skim milk]

hmmm.. not really sure how to apply that.

Can anyone introduce me to the beginning steps? I think I can figure it out after that. I would ask my Professor but he never responds to my emails

 

[chuckywang]

Your parallel plane would have the form of:

x+3y-z = C where C is some constant.

Now all you have to do is calculate C. To do this, pick a point on one plane and figure out the distance of that point to the other plane. Set that equal to 2 and solve for C.