UPSC NDA Math Model Paper 5

Given: Equation of planes is: 2x−y+3z+4=0 and 6x−3y+9z−3=0
The given equations can be re-written as: 2x−y+3z+4=0 and 2x−y+3z−1=0
As we can see that, both the planes are parallel to each other and the distance between two parallel planes is given by: |

d1−d2

√a2+b2+c2

|
Here, a=2,b=−1,c=3,d1=4 and d2=−1
⇒|

4+1

√22+(−1)2+32

| =

5

√14