What is the distance between two parallel planes?

[385sk117]

Homework Statement

1. Find the distance betwwen the parallel palnes:

a) x + y + 2z = 4 and 2x + 2y + 4z +11 = 0
b) ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0

2.Find the equations of the two planes which are parallel to 2x - y + 2z = 5 and 2 unit from it

Homework Equations

The Attempt at a Solution

I think i should find any point on one of the plane and using that to find the perpendicular line between two planes which will give the distance between them, but how can i find a point on the plane from the equation given to me?

 

[danago]

Pick any x and y you want, plug them into the equation for the plane and then solve for z, and you will have a point on the plane.

 

[385sk117]

oh, so if there isn't any restriction then i can choose any value of x and y on the plane?
Thankyou :)

 

[danago]

oh, so if there isn't any restriction then i can choose any value of x and y on the plane?
Thankyou :)

Well since no restrictions have been made on the planes, they "stretch" over every possible x and y value. Its a bit like a line in the x-y plane; Unless its domain has been restricted, it will cross over every single real x value and have a corrosponding y value there.