## rock_mit182 one year ago find the distance between the parallel planes: a) 2x +y -2z =0 and 2x+y -2z =5

1. happy_to_help

Is that how the question is written?

2. rock_mit182

In Exercises 37 and 38, find the distance between the parallel planes. 37. 2x + y - 2z = 0 and 2x + y - 2z = 5

3. happy_to_help

This is the formula you have to use

4. rock_mit182

I guess i need that creepy formula: "In the case where the line £ is in IR2 and its equation has the general form ax + by = c, the distance d(B, €) from B = (x0, y0) is given by the formula"

5. happy_to_help

They dont give you a graph?

6. rock_mit182

$d(\beta,\iota) = \frac{ |a x_{0} + b y_{0}+ c| }{\sqrt{a ^{2}+b ^{2}} }$

7. rock_mit182

no, they don't give anything. But i guess it would be something like:|dw:1443017717632:dw|

8. rock_mit182

@texaschic101 @inkyvoyd Could you give me a hand on this one..

9. rock_mit182

@paki @welshfella

10. rock_mit182

In general, the distance d(B, <JP) from the point B = (x0, y0, z0) to the plane whose general equation is ax + by + cz = d is given by the formula: $d(\beta, Plane) = \frac{ |ax _{0}+ by _{0}+ c z _{0} - d |}{ \sqrt{a ^{2}+b ^{2}+c ^{2}} }$

11. welshfella

first you must find a point that lies on one of the planes for the first equation x = y = z = 0 so there is the point (0,0,0) on that plane

12. welshfella

so now you can use your formula

13. rock_mit182

that's all ?

14. rock_mit182

what if use a point of the other plane should i get the same answer ?

15. welshfella

x0 y0 and z0 = 0 d = 5

16. welshfella

yes I've never come across this formula before but i dont see why not Its easy to use (0,0,0) though

17. welshfella

the numerator will be 5 and plug in a = 2 , b = 1 and c = -2

18. rock_mit182

ok it seems easy... could you help me with this one: Find the normal form of the equation of the plane that passes through P = (O, - 2, 5 ) and is parallel to the plane with general equation 6x - y + 2z = 3 .

19. welshfella

I'd have to look all that stuff up I'm afraid but i haven't got the time at the moment.

20. rock_mit182

ok fine, thanks anyway